%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@Comment{ The Arithmetic of Dynamical Systems }
@Comment{ Joseph H. Silverman }
@Comment{ Biblographic Database File - ArithDyn.bib }

@comment{

*** Are all of Zieve's dynamics articles joint?

Articles preceded by
comment{UPDATE}
are preprints or "to appears" that should be updated as appropriate.
}

@comment{
%%% To fix excessive space between bibliography entries, 
%%% after creating the .bbl file using bibtex, put the following
%%% three commands after the \begin{bibliography} command. (May need
%%% to adjust the size of \itemsep to look okay.)
\setlength{\itemsep}{-4pt}
\small
\addcontentsline{toc}{chapter}{Bibliography} % not needed for amsbook.sty
}

@comment{ ------------------------------------------------------------ }
@comment{ Material to Add:

}

@comment{ ----- Blank form for ArXiv papers ---}
@comment{UPDATE}
@misc {arxiv,
    AUTHOR = {},
    TITLE = {},
     YEAR = {},
     NOTE = {\url{}},
}

@comment{ ------------------------------------------------------------ }

@comment{--AAA-- }

@book {MR510197,
    AUTHOR = {Ahlfors, Lars V.},
     TITLE = {Complex {A}nalysis},
 PUBLISHER = {McGraw-Hill Book Co.},
   ADDRESS = {New York},
      YEAR = {1978},
     PAGES = {xi+331},
      ISBN = {0-07-000657-1},
   MRCLASS = {30-01},
  MRNUMBER = {MR510197 (80c:30001)},
}
@comment{UPDATE}
@misc {arxiv0910.4556,
    AUTHOR = {Ahmadi, Omran},
    TITLE = {A Note on Stable Quadratic Polynomials over Fields 
          of Characteristic Two},
     YEAR = {2009},
     NOTE = {\url{arXiv:0910.4556}},
}
@article {MR0335427,
    AUTHOR = {Aho, A. V. and Sloane, N. J. A.},
     TITLE = {Some doubly exponential sequences},
   JOURNAL = {Fibonacci Quart.},
  FJOURNAL = {The Fibonacci Quarterly. Official Organ of the Fibonacci
              Association},
    VOLUME = {11},
      YEAR = {1973},
    NUMBER = {4},
     PAGES = {429--437},
      ISSN = {0015-0517},
   MRCLASS = {10A40},
  MRNUMBER = {MR0335427 (49 \#209)},
MRREVIEWER = {J. B. Roberts},
}
@comment{http://www.research.att.com/~njas/doc/doubly.html, Publ. List, item 20}

@article {arxiv0408170,
   AUTHOR = {Aitken, Wayne and Hajir, Farshid and Maire, Christian},
    TITLE = {Finitely ramified iterated extensions},
   JOURNAL = {IMRN},
  FJOURNAL = {International Mathematics Research Notices},
     YEAR = {2005},
    PAGES = {855--880},
   VOLUME = {14},
}
@comment{\url{ArXiv:math.NT/0408170}}

@comment{UPDATE}
@misc {akbaryghioca09,
    AUTHOR = {Akbary, Amir and Ghioca, Dragos},
    TITLE = {Periods of orbits modulo primes},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
   COMMENT = {to appear, preprint 2009}
}

@article {MR1840304,
    AUTHOR = {Albeverio, S. and Tirotstsi, B. and Khrennikov, A.
              Yu. and de Shmedt, S.},
     TITLE = {{$p$}-adic dynamical systems},
   JOURNAL = {Teoret. Mat. Fiz.},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Teoreticheskaya i
              Matematicheskaya Fizika},
    VOLUME = {114},
      YEAR = {1998},
    NUMBER = {3},
     PAGES = {349--365},
      ISSN = {0564-6162},
   MRCLASS = {37B99 (11S85)},
  MRNUMBER = {MR1840304 (2002a:37018)},
}

@article {MR1928725,
    AUTHOR = {Albeverio, S. and Gundlach, M. and Khrennikov, A. and Lindahl,
              K.-O.},
     TITLE = {On the {M}arkovian behavior of {$p$}-adic random dynamical
              systems},
   JOURNAL = {Russ. J. Math. Phys.},
  FJOURNAL = {Russian Journal of Mathematical Physics},
    VOLUME = {8},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {135--152},
      ISSN = {1061-9208},
   MRCLASS = {60J10 (37H99 81Q99)},
  MRNUMBER = {MR1928725 (2003g:60124)},
MRREVIEWER = {Yves Lacroix},
}

@article {MR2163517,
    AUTHOR = {Ali, Nidal},
     TITLE = {Stabilit\'e des polyn\^omes},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {119},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {53--63},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11R09 (11T06 12E05)},
  MRNUMBER = {MR2163517 (2006h:11125)},
MRREVIEWER = {Peter M{\"u}ller},
}
@comment{The polynomial f is said to be stable if f^m is
irreducible for all positive integers m.}

@comment{UPDATE}
@misc {arxiv0802.2938,
    AUTHOR = {Aliev, Iskander and Smyth, Chris },
    TITLE = {Power maps and subvarieties of the complex algebraic $n$-torus},
     YEAR = {2008},
     NOTE = {\url{ arXiv:0802.2938}},
}

@article {MR1817715,
    AUTHOR = {Amoroso, Francesco and Zannier, Umberto},
     TITLE = {A relative {D}obrowolski lower bound over abelian extensions},
   JOURNAL = {Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)},
  FJOURNAL = {Annali della Scuola Normale Superiore di Pisa. Classe di
              Scienze. Serie IV},
    VOLUME = {29},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {711--727},
      ISSN = {0391-173X},
     CODEN = {PSNAAI},
   MRCLASS = {11G50 (11J99 11R47)},
  MRNUMBER = {MR1817715 (2003a:11078)},
}
@article {MR1740514,
    AUTHOR = {Amoroso, Francesco and Dvornicich, Roberto},
     TITLE = {A lower bound for the height in abelian extensions},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {80},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {260--272},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11R18 (11G50)},
  MRNUMBER = {MR1740514 (2001b:11100)},
MRREVIEWER = {Christopher Smyth},
}

@incollection {arxiv0602083,
    AUTHOR = {Anashin, Vladimir},
     TITLE = {Ergodic transformations in the space of {$p$}-adic integers},
 BOOKTITLE = {$p$-adic mathematical physics},
    SERIES = {AIP Conf. Proc.},
    VOLUME = {826},
     PAGES = {3--24},
 PUBLISHER = {Amer. Inst. Phys.},
   ADDRESS = {Melville, NY},
      YEAR = {2006},
   MRCLASS = {37A45 (11S85 37A25)},
  MRNUMBER = {MR2258670},
}
@comment{\url{ArXiv:math.math.DS/0602083}}

@article {MR2220002,
    AUTHOR = {Angl{\`e}s d'Auriac, J.-Ch. and Maillard, J.-M. and Viallet,
              C. M.},
     TITLE = {On the complexity of some birational transformations},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {39},
      YEAR = {2006},
    NUMBER = {14},
     PAGES = {3641--3654},
      ISSN = {0305-4470},
     CODEN = {JPHAC5},
   MRCLASS = {37F10 (14Q99 20F55 37B99)},
  MRNUMBER = {MR2220002 (2006m:37061)},
MRREVIEWER = {Eric Bedford},
}

@book {apostol:utm, 
    AUTHOR = {Apostol, Tom M.},
     TITLE = {Introduction to {A}nalytic {N}umber {T}heory},
      NOTE = {Undergraduate Texts in Mathematics},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1976},
     PAGES = {xii+338},
   MRCLASS = {10-01 (10AXX 10HXX)},
  MRNUMBER = {MR0434929 (55 \#7892)},
MRREVIEWER = {E. Grosswald},
}

@article {MR2163516,
    AUTHOR = {Arias de Reyna, J.},
     TITLE = {Dynamical zeta functions and {K}ummer congruences},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {119},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {39--52},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11B68 (11A07 11B37 37C30)},
  MRNUMBER = {MR2163516 (2006d:11020)},
MRREVIEWER = {Thomas Ward},
}
	
@comment {MR1264116}
@article {arrowsmith:padicsiegeldisk,
    AUTHOR = {Arrowsmith, David K. and Vivaldi, Franco},
     TITLE = {Geometry of {$p$}-adic {S}iegel discs},
   JOURNAL = {Phys. D},
  FJOURNAL = {Physica D. Nonlinear Phenomena},
    VOLUME = {71},
      YEAR = {1994},
    NUMBER = {1-2},
     PAGES = {222--236},
      ISSN = {0167-2789},
     CODEN = {PDNPDT},
   MRCLASS = {11S85 (11S31 58F99)},
  MRNUMBER = {MR1264116 (95d:11162)},
MRREVIEWER = {Evgenii I. Zelenov},
}

@comment {MR1218804}
@article {arrowsmith:padichorseshoe,
    AUTHOR = {Arrowsmith, David K. and Vivaldi, Franco},
     TITLE = {Some {$p$}-adic representations of the {S}male horseshoe},
   JOURNAL = {Phys. Lett. A},
  FJOURNAL = {Physics Letters. A},
    VOLUME = {176},
      YEAR = {1993},
    NUMBER = {5},
     PAGES = {292--294},
      ISSN = {0375-9601},
     CODEN = {PYLAAG},
   MRCLASS = {58F03 (11Z50 32P05)},
  MRNUMBER = {MR1218804 (94c:58054)},
MRREVIEWER = {Evgenii I. Zelenov},
}

@article {MR2017146,
    AUTHOR = {Autissier, Pascal},
     TITLE = {Hauteur des correspondances de {H}ecke},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {131},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {421--433},
      ISSN = {0037-9484},
     CODEN = {BSMFAA},
   MRCLASS = {11G18 (11F32 11G50 14G40)},
  MRNUMBER = {MR2017146 (2004i:11058)},
MRREVIEWER = {Robin de Jong},
}
@comment {\url{ArXiv:math.NT/0404355}}

@article {autissierpreprint04,
    AUTHOR = {Autissier, Pascal},
     TITLE = {Dynamique des correspondances alg\'ebriques et hauteurs},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2004},
    NUMBER = {69},
     PAGES = {3723--3739},
      ISSN = {1073-7928},
   MRCLASS = {14G40 (11G50)},
  MRNUMBER = {MR2099499},
MRREVIEWER = {Robin de Jong},
}

@article {MR1760091,
    AUTHOR = {Ayad, Mohamed and McQuillan, Donald L.},
     TITLE = {Irreducibility of the iterates of a quadratic polynomial over
              a field},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {93},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {87--97},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11C08 (11R09 11T06 12E10)},
  MRNUMBER = {MR1760091 (2001c:11031)},
MRREVIEWER = {Michel Grandcolas},
}
@article {MR1845367,
    AUTHOR = {Ayad, Mohamed and McQuillan, Donald L.},
     TITLE = {Corrections to: ``{I}rreducibility of the iterates of a
              quadratic polynomial over a field'' [{A}cta {A}rith.\ \textbf{93}
              (2000), no. 1, 87--97]},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {99},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {97},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11R09 (11T06 12E10)},
  MRNUMBER = {MR1845367 (2002d:11125)},
}

@article {MR1242609,
    AUTHOR = {Ayad, Mohamed},
     TITLE = {P\'eriodicit\'e (mod {$q$}) des suites elliptiques et points
              {$S$}-entiers sur les courbes elliptiques},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {43},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {585--618},
      ISSN = {0373-0956},
     CODEN = {AIFUA7},
   MRCLASS = {11B50 (11B83 11D25 11G05)},
  MRNUMBER = {MR1242609 (94f:11009)},
MRREVIEWER = {Franck Lepr{\'e}vost},
}

@comment{--BBB-- }

@incollection {MR0277001,
    AUTHOR = {Banchoff, Thomas F. and Rosen, Michael I.},
     TITLE = {Periodic points of {A}nosov diffeomorphisms},
 BOOKTITLE = {Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley,
              Calif., 1968)},
     PAGES = {17--21},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, R.I.},
      YEAR = {1970},
   MRCLASS = {57.48 (34.00)},
  MRNUMBER = {MR0277001 (43 \#2738)},
MRREVIEWER = {J. W. Robbin},
}

@article {MR0169989,
    AUTHOR = {Baker, I. N.},
     TITLE = {Fixpoints of polynomials and rational functions},
   JOURNAL = {J. London Math. Soc.},
    VOLUME = {39},
      YEAR = {1964},
     PAGES = {615--622},
   MRCLASS = {30.10},
  MRNUMBER = {MR0169989 (30 \#230)},
MRREVIEWER = {W. J. Thron},
}
@comment{see also Kisaka for representatives of the exceptional maps, and
for characteristic p, see Pezda}

@comment{UPDATE}
@misc {arxiv0606252,
   AUTHOR = {Baker, Matthew},
    TITLE = {Uniform structures and {B}erkovich spaces},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.NT/0606252}},
}
@comment{16 pages ? is this ever going to appear?}

@article {arxiv0507484,
    AUTHOR = {Baker, Matthew},
     TITLE = {A lower bound for average values of dynamical {G}reen's
              functions},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {13},
      YEAR = {2006},
    NUMBER = {2-3},
     PAGES = {245--257},
      ISSN = {1073-2780},
   MRCLASS = {14Gxx (11Gxx)},
  MRNUMBER = {MR2231115},
}
@comment{\url{ArXiv:math.NT/0507484}}

@comment{UPDATE}
@article {arxiv0601046,
    AUTHOR = {Baker, Matthew},
     TITLE = {A finiteness theorem for canonical heights attached to
              rational maps over function fields},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {626},
      YEAR = {2009},
     PAGES = {205--233},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {14Gxx (11G50 11R58)},
  MRNUMBER = {MR2492995},
}

@misc {arxiv0305181,
   AUTHOR = {Baker, Matthew and Hsia, Liang-Chung},
     TITLE = {Canonical heights, transfinite diameters, and polynomial
              dynamics},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {585},
      YEAR = {2005},
     PAGES = {61--92},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G50 (37A45 37F10)},
  MRNUMBER = {MR2164622 (2006i:11071)},
MRREVIEWER = {Clayton Petsche},
}
@comment{ArXiv:math.NT/0305181, 28 pages}

@article {MR2114791,
    AUTHOR = {Baker, Matthew and Ih, Su-ion},
     TITLE = {Equidistribution of small subvarieties of an abelian variety},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {10},
      YEAR = {2004},
     PAGES = {279--285 (electronic)},
      ISSN = {1076-9803},
   MRCLASS = {11G10 (11G35 14K12 14K15)},
  MRNUMBER = {MR2114791 (2005h:11116)},
MRREVIEWER = {Robin de Jong},
}

@article {arxiv0509485,
    AUTHOR = {Baker, Matthew and Ih, Su-ion and Rumely, Robert},
     TITLE = {A finiteness property of torsion points},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {2},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {217--248},
      ISSN = {1937-0652},
   MRCLASS = {11G50 (11G05 11J71 11J86)},
  MRNUMBER = {MR2377370 (2009g:11078)},
MRREVIEWER = {Clayton Petsche},
}

@comment{UPDATE}
@misc {arxiv0407433,
   AUTHOR = {Baker, Matthew and Rumely, Robert},
    TITLE = {Analysis and dynamics on the {B}erkovich projective line},
     YEAR = {2004},
     NOTE = {\url{ArXiv:math.NT/0407433}},
}
@comment{150 pages, these notes have been subsumed by their book}

@comment{UPDATE}
@misc {bakerrumelyberkbook,
   AUTHOR = {Baker, Matthew and Rumely, Robert},
    TITLE = {Potential Theory on the {B}erkovich Projective Line},
     YEAR = {2006},
     NOTE = {\url{http://www.math.gatech.edu/~mbaker/pdf/BerkBook.pdf},
                     in preparation},
}
@comment{268 pages}

@comment{UPDATE}
@misc {bakerrumelymontel2005,
   AUTHOR = {Baker, Matthew and Rumely, Robert},
    TITLE = {Montel's theorem for the {B}erkovich projective line and the
                 {B}erkovich {J}ulia set of a rational map},
     YEAR = {2005},
     NOTE = {Preprint},
}
@comment{31 pages ? is this ever going to appear?}

@article {arxiv0407427,
    AUTHOR = {Baker, Matt and Rumely, Robert},
     TITLE = {Harmonic analysis on metrized graphs},
   JOURNAL = {Canad. J. Math.},
  FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de
              Math\'ematiques},
    VOLUME = {59},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {225--275},
      ISSN = {0008-414X},
     CODEN = {CJMAAB},
   MRCLASS = {43A99 (05C12 58C40)},
  MRNUMBER = {MR2310616 (2008h:43019)},
MRREVIEWER = {Charles Favre},
}


@article {arxiv0407426,
   AUTHOR = {Baker, Matthew and Rumely, Robert},
     TITLE = {Equidistribution of small points, rational dynamics, and
              potential theory},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {56},
      YEAR = {2006},
    NUMBER = {3},
     PAGES = {625--688},
      ISSN = {0373-0956},
     CODEN = {AIFUA7},
   MRCLASS = {11G50 (37A45 37F10)},
  MRNUMBER = {MR2244226}, 
}
@comment{ArXiv:math.NT/0407426, 53 pages}

@article {baragarluijk06,
    AUTHOR = {Baragar, Arthur and van Luijk, Ronald},
     TITLE = {{$K3$} surfaces with {P}icard number three and canonical
              vector heights},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {76},
      YEAR = {2007},
    NUMBER = {259},
     PAGES = {1493--1498 (electronic)},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {14J28 (11G50 14C22 14G10 14J10)},
  MRNUMBER = {MR2299785 (2008e:14055)},
MRREVIEWER = {Matthias Sch{\"u}tt},
}

@article {MR2059748,
    AUTHOR = {Baragar, Arthur},
     TITLE = {Canonical vector heights on {$K3$} surfaces with {P}icard
              number three---an argument for nonexistence},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {73},
      YEAR = {2004},
    NUMBER = {248},
     PAGES = {2019--2025 (electronic)},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {14J28 (11G50 14G25)},
  MRNUMBER = {MR2059748 (2005e:14058)},
MRREVIEWER = {Yuri Tschinkel},
}
@article {MR2011389,
    AUTHOR = {Baragar, Arthur},
     TITLE = {Canonical vector heights on algebraic {$K3$} surfaces with
              {P}icard number two},
   JOURNAL = {Canad. Math. Bull.},
  FJOURNAL = {Canadian Mathematical Bulletin. Bulletin Canadien de
              Math\'ematiques},
    VOLUME = {46},
      YEAR = {2003},
    NUMBER = {4},
     PAGES = {495--508},
      ISSN = {0008-4395},
     CODEN = {CMBUA3},
   MRCLASS = {11G50 (11G35 14G40 14J28)},
  MRNUMBER = {MR2011389 (2004i:11065)},
MRREVIEWER = {Noriko Yui},
}
@article {MR1985002,
    AUTHOR = {Baragar, Arthur},
     TITLE = {Orbits of curves on certain {$K3$} surfaces},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {137},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {115--134},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11G35 (14J28)},
  MRNUMBER = {MR1985002 (2004d:11050)},
MRREVIEWER = {Noriko Yui},
}
@article {MR1459107,
    AUTHOR = {Baragar, Arthur},
     TITLE = {Rational curves on {$K3$} surfaces in {$\mathbb{P}\sp 1
              \times\mathbb{P}\sp 1\times\mathbb{P}\sp 1$}},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {126},
      YEAR = {1998},
    NUMBER = {3},
     PAGES = {637--644},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {14G05 (14J20 14J28)},
  MRNUMBER = {MR1459107 (98h:14028)},
MRREVIEWER = {Dan Abramovich},
}
@article {MR1397435,
    AUTHOR = {Baragar, Arthur},
     TITLE = {Rational points on {$K3$} surfaces in 
             {$\mathbb{P}\sp 1\times\mathbb{P}\sp 1\times\mathbb{P}\sp 1$}},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {305},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {541--558},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {14G05 (14J28)},
  MRNUMBER = {MR1397435 (97g:14020)},
MRREVIEWER = {Lin Weng},
}

@article {MR1302308,
    AUTHOR = {Baragar, Arthur},
     TITLE = {Asymptotic growth of {M}arkoff-{H}urwitz numbers},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {94},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {1--18},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11D72 (11J06)},
  MRNUMBER = {MR1302308 (95i:11025)},
MRREVIEWER = {Joseph H. Silverman},
}
@article {MR1295950,
    AUTHOR = {Baragar, Arthur},
     TITLE = {Integral solutions of {M}arkoff-{H}urwitz equations},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {49},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {27--44},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11J06},
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@book {MR2030225,
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@article {batramorton:algebraicdynamics,
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MRREVIEWER = {S. D. Cohen},
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@comment {MR1128089}
@book{beardon:gtm, 
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  MRNUMBER = {MR1128089 (92j:30026)},
MRREVIEWER = {A. {\`E}. Eremenko},
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@book {MR1406314,
    AUTHOR = {Beauville, Arnaud},
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 PUBLISHER = {Cambridge University Press},
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   MRCLASS = {14Jxx (14-02)},
  MRNUMBER = {MR1406314 (97e:14045)},
}



@article {MR2449533,
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   JOURNAL = {Ergodic Theory Dynam. Systems},
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    VOLUME = {28},
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    NUMBER = {5},
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  MRNUMBER = {MR2449533},
MRREVIEWER = {Charles Favre},
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@article {MR2428100,
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@article  {arxiv0512507,
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MRREVIEWER = {Jeffrey Diller},
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@article {MR2280499,
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@article {MR2111418,
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@book {MR1781937,
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@comment{UPDATE}
@misc {arxiv:0808.3266,
    AUTHOR = {Bell, Jason and Ghioca, Dragos and Tucker, Thomas},
    TITLE = {The dynamical {M}ordell--{L}ang problem for {\'e}tale maps},
     YEAR = {2008},
     NOTE = {\url{arXiv:0808.3266}},
}

@article {MR1704282,
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   MRCLASS = {37D45 (37A35 37C99 39A12)},
  MRNUMBER = {MR1704282 (2000f:37040)},
MRREVIEWER = {Remo Badii},
}

@UNPUBLISHED{unpubBenMenahem,
 AUTHOR  = {Ben-Menahem, Shahar},
 TITLE   = {$p$-adic iterations},
 NOTE    = {Preprint, {TAUP} 1627--88, {T}el-{A}viv {University}},
 YEAR    = {1988}
}

@phdthesis{benedetto:thesis, 
    AUTHOR = {Benedetto, Robert L.},
    TITLE = {Fatou components in $p$-adic dynamics},
   SCHOOL = {Brown University},
     YEAR = {1998}
}

@article {MR1981035,
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  MRNUMBER = {MR1981035 (2004a:30042)},
MRREVIEWER = {William A. Cherry},
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@article {MR1941304,
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  MRNUMBER = {MR1941304 (2003i:37040)},
MRREVIEWER = {Serge Cantat},
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@comment{MR2157374}
@article {arxiv0312034,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Wandering domains and nontrivial reduction in
              non-{A}rchimedean dynamics},
   JOURNAL = {Illinois J. Math.},
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  MRNUMBER = {MR2157374 (2006e:11185)},
MRREVIEWER = {Charles Favre},
}

@article {arxiv0312029,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Wandering domains in non-{A}rchimedean polynomial dynamics},
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  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {38},
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   MRCLASS = {12J25 (37Bxx 37Fxx)},
  MRNUMBER = {MR2285248},
}

@article {arxiv0510444,
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      YEAR = {2005},
    NUMBER = {62},
     PAGES = {3855--3866},
      ISSN = {1073-7928},
   MRCLASS = {11G50 (11R58)},
  MRNUMBER = {MR2202175},
MRREVIEWER = {Clayton Petsche},
}

@article {MR1863402,
    AUTHOR = {Benedetto, Robert L.},
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  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
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  MRNUMBER = {MR1863402 (2002k:11215)},
MRREVIEWER = {Michael E. Zieve},
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@article {MR1864055,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {An elementary product identity in polynomial dynamics},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {108},
      YEAR = {2001},
    NUMBER = {9},
     PAGES = {860--864},
      ISSN = {0002-9890},
     CODEN = {AMMYAE},
   MRCLASS = {11C08 (11R27 13B25 37F10)},
  MRNUMBER = {MR1864055 (2003g:11021)},
MRREVIEWER = {Peter Ha{\"{\i}}ssinsky},
}
@article {benedetto:hyperbolic,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Hyperbolic maps in {$p$}-adic dynamics},
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    NUMBER = {1},
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      ISSN = {0143-3857},
   MRCLASS = {11S99 (37D99)},
  MRNUMBER = {MR1826658 (2002c:11163)},
MRREVIEWER = {Michael E. Zieve},
}
@article {MR1813109,
    AUTHOR = {Benedetto, Robert L.},
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  MRNUMBER = {MR1813109 (2001m:11211)},
MRREVIEWER = {Serge Cantat},
}
@article {MR1781331,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {{$p$}-adic dynamics and {S}ullivan's no wandering domains
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   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {122},
      YEAR = {2000},
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   MRCLASS = {37F10 (11S99 37F50 37F99)},
  MRNUMBER = {MR1781331 (2001f:37054)},
MRREVIEWER = {Serge Cantat},
}

@article {arxiv0506480,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Preperiodic points of polynomials over global fields},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {608},
      YEAR = {2007},
     PAGES = {123--153},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G35 (37Bxx 37F10)},
  MRNUMBER = {MR2339471},
}

@comment{*** Title of Benedetto's book is tentative}
@comment{UPDATE}
@book {benedettobook,
    AUTHOR = {Benedetto, Robert L.},
     TITLE = {Dynamics in one $p$-adic variable},
      NOTE = {In preparation, 2007},
}
@comment{UPDATE}
@misc {arxiv0807.0468,
    AUTHOR = {Benedetto, Robert L. and Dickman, Benjamin and Joseph, Sasha
         and Krause, Benjamin and Rubin, Daniel and Zhou, Xinwen},
    TITLE = {Computing points of small height for cubic polynomials},
     YEAR = {2008},
     NOTE = {\url{arXiv:0807.0468}},
}
@comment{UPDATE}
@misc {arXiv:0712.2344,
    AUTHOR = {Benedetto, Robert L. and Ghioca, Dragos and Kurlberg, Par 
            and Tucker, Thomas},
    TITLE = {The Dynamical {M}ordell-{L}ang Conjecture},
     YEAR = {2007},
     NOTE = {\url{arXiv:0712.2344}},
}
@comment{UPDATE}
@misc {arXiv0810.1086,
    AUTHOR = {Benedetto, Robert L. and Ghioca, Dragos and Kurlberg, Par 
            and Tucker, Thomas},
    TITLE = {A gap principle for dynamics},
     YEAR = {2008},
     NOTE = {\url{arXiv:0810.1086}},
}
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MRREVIEWER = {John H. Jaroma},
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@book {MR1070709,
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@article {MR1259429,
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}

@preamble{
   "\def\cprime{$'$} "
}
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@inproceedings {MR1648064,
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MRREVIEWER = {Annette Werner},
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@article {MR1871293,
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@article {MR2051375,
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@article {MR2031456,
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MRREVIEWER = {L. Carlitz},
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@book {bombierigubler,
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     PAGES = {668},
      YEAR = {2006},
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@article {MR1793690,
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  MRNUMBER = {MR1793690 (2003g:32035)},
MRREVIEWER = {Vincent Guedj},
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@book {MR0195803,
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 PUBLISHER = {Academic Press},
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  MRNUMBER = {MR0195803 (33 \#4001)},
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     TITLE = {A map on the space of rational functions},
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  FJOURNAL = {The Rocky Mountain Journal of Mathematics},
    VOLUME = {35},
      YEAR = {2005},
    NUMBER = {6},
     PAGES = {1861--1880},
      ISSN = {0035-7596},
     CODEN = {RMJMAE},
   MRCLASS = {33B99 (05E35 39B12)},
  MRNUMBER = {MR2210638},
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     TITLE = {A transformation of rational functions},
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  FJOURNAL = {Elemente der Mathematik. Eine Zeitschrift der Schweizerischen
              Mathematischen Gesellschaft. Une Revue de la Soci\'et\'e
              Math\'ematique Suisse. Una Rivista della Societ\`a Matematica
              Svizzera},
    VOLUME = {58},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {73--83},
      ISSN = {0013-6018},
     CODEN = {ELMMAF},
   MRCLASS = {33E05},
  MRNUMBER = {MR1980323 (2004e:33022)},
MRREVIEWER = {Matti Vuorinen},
}
@comment{See also
Briscoe, S. - Jimenez, L. - Medina, L.: Asymptotics of a
transformation on the space of rational functions. SIMU 2002, Report.
Briscoe, S. - Jimenez, L. - Manna, D. - Medina, L. - Moll, V.: The
dynamics of a transformation on the space of rational functions. In
preparation.
}
@book {bosch:nonarchanalysis, 
    AUTHOR = {Bosch, S. and G{\"u}ntzer, U. and Remmert, R.},
     TITLE = {Non-{A}rchimedean analysis},
    SERIES = {Grundlehren der Mathematischen Wissenschaften},
    VOLUME = {261},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1984},
     PAGES = {xii+436},
      ISBN = {3-540-12546-9},
   MRCLASS = {32K10 (30G05 46P05)},
  MRNUMBER = {MR746961 (86b:32031)},
MRREVIEWER = {W. Bartenwerfer},
}

@comment {MR1734635}
@article {bosio:roundoff,
    AUTHOR = {Bosio, D. and Vivaldi, F.},
     TITLE = {Round-off errors and {$p$}-adic numbers},
   JOURNAL = {Nonlinearity},
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    VOLUME = {13},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {309--322},
      ISSN = {0951-7715},
     CODEN = {NONLE5},
   MRCLASS = {37M99 (11S85 37B10 37E99 65G50)},
  MRNUMBER = {MR1734635 (2000k:37130)},
MRREVIEWER = {M. L. Blank},
}
@article {MR2318536,
    AUTHOR = {Boston, Nigel and Jones, Rafe},
     TITLE = {Arboreal {G}alois representations},
   JOURNAL = {Geom. Dedicata},
  FJOURNAL = {Geometriae Dedicata},
    VOLUME = {124},
      YEAR = {2007},
     PAGES = {27--35},
      ISSN = {0046-5755},
     CODEN = {GEMDAT},
   MRCLASS = {11F80 (11R32 20E08 20E18)},
  MRNUMBER = {MR2318536 (2009e:11103)},
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@phdthesis{bousch:thesis, 
   AUTHOR = {T. Bousch},
    TITLE = {Sur quelques probl{\`{e}}mes de dynamique holomorphe},
   SCHOOL = {Universit{\'{e}} de Paris-Sud},
  ADDRESS = {Centre d'Orsay},
     YEAR = {1992}
	}

@article{boyd:mahlermeasure,
    AUTHOR = {Boyd, David W.},
     TITLE = {Mahler's measure and special values of {$L$}-functions},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {7},
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    NUMBER = {1},
     PAGES = {37--82},
      ISSN = {1058-6458},
   MRCLASS = {11G40 (11R06 11Y35)},
  MRNUMBER = {MR1618282 (99d:11070)},
MRREVIEWER = {Jan Nekov{\'a}{\v{r}}},
}

@comment{UPDATE}
@misc {arxiv0511442,
   AUTHOR = {Broise, Anne and Paulin, Fr\'{e}d\'{e}ric},
    TITLE = {Dynamique sur le rayon modulaire et fractions 
              continues en caract\'{e}ristique $p$},
     YEAR = {2005},
     NOTE = {\url{ArXiv:math.GR/0511442}},
   MRCLASS = {11J70},
}
@comment{21 pages}

@article {bryksilva05,
    AUTHOR = {Bryk, John and Silva, Cesar E.},
     TITLE = {Measurable dynamics of simple {$p$}-adic polynomials},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {112},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {212--232},
      ISSN = {0002-9890},
     CODEN = {AMMYAE},
   MRCLASS = {37A45 (11Sxx 54H20)},
  MRNUMBER = {MR2125384},
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@article {MR2171197,
    AUTHOR = {Buium, Alexandru},
     TITLE = {Complex dynamics and invariant forms mod {$p$}},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2005},
    NUMBER = {31},
     PAGES = {1889--1899},
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   MRCLASS = {11Gxx (14Gxx 37F10)},
  MRNUMBER = {MR2171197},
       DOI = {10.1155/IMRN.2005.1889},
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@comment{\url{ArXiv:math.DS/0505037}}

@article {buiumpreprint050704,
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      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11Gxx (37Fxx)},
  MRNUMBER = {MR2130591},
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@comment{--CCC-- }

@article {callgoldstine:htonprojspace,
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@article {arxiv0504533,
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   JOURNAL = {Monatsh. Math.},
  FJOURNAL = {Monatshefte f\"ur Mathematik},
    VOLUME = {149},
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@article {arxiv0512338, 
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    VOLUME = {18},
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  MRNUMBER = {MR2352676 (2008k:11073)},
MRREVIEWER = {W. Narkiewicz},
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@comment{UPDATE}
@misc {Canci07,
   AUTHOR = {Canci, Jung Kyu},
    TITLE = {Rational periodic points for quadratic maps},
     YEAR = {2008},
     NOTE = {\url{arXiv:0801.4636}},
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@article {MR1864630,
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MRREVIEWER = {Eric Bedford},
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MRREVIEWER = {Christopher Smyth},
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      YEAR = {1986},
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@book {MR1144763,
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@article {arxiv0304023,
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  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {595},
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      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {14Gxx},
  MRNUMBER = {MR2244803},
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@comment{\url{ArXiv:math.NT/0304023}}

@comment{UPDATE}
@misc {arxiv0812.0944,
    AUTHOR = {Chambert-Loir, Antoine},
    TITLE = {Th{\'e}or{\`e}mes d'{\'e}quidistribution pour les syst{\`e}mes
         dynamiques d'origine arithm{\'e}tique},
     YEAR = {2008},
     NOTE = {\url{arXiv:0812.0944}},
}

@article {MR2244803,
    AUTHOR = {Chambert-Loir, Antoine},
     TITLE = {Mesures et \'equidistribution sur les espaces de {B}erkovich},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {595},
      YEAR = {2006},
     PAGES = {215--235},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {14G40 (14G25)},
  MRNUMBER = {MR2244803 (2008b:14040)},
}

@comment{UPDATE}
@misc {arxiv0612556,
   AUTHOR = {Chambert-Loir, Antoine and Thuillier, Amaury},
    TITLE = {Formule de {M}ahler et {\'e}quidistribution logarithmique},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.NT/0612556}},
}
@comment{24 pages}

@article {MR850926,
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  FJOURNAL = {Discrete Mathematics},
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MRREVIEWER = {N. Popescu},
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@article {arxiv0711.3864,
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     TITLE = {Difference fields and descent in algebraic dynamics. {I}},
   JOURNAL = {J. Inst. Math. Jussieu},
  FJOURNAL = {Journal of the Institute of Mathematics of Jussieu. JIMJ.
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     PAGES = {653--686},
      ISSN = {1474-7480},
   MRCLASS = {03C60 (12H10 14Gxx 37Fxx)},
  MRNUMBER = {MR2469450},
}

@comment{UPDATE}
@misc {arxiv0711.3865,
    AUTHOR = {Chatzidakis, Zo{\'e} and Hrushovski, Ehud},
    TITLE = {Difference fields and descent in algebraic dynamics {II}},
     YEAR = {2008},
     NOTE = {\url{arxiv.org/abs/arXiv:0711.3865}},
}

@article {MR2072394,
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MRREVIEWER = {Serge{\u\i} V. Konyagin},
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@article {arxivDS0605439,
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@article {MR2080121,
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  MRNUMBER = {MR2080121 (2005g:58055)},
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@proceedings {MR1943523,
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  MRNUMBER = {MR1943523 (2003g:30001)},
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@article {Chowla33,
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@book {MR1728313,
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MRREVIEWER = {Yu Wang},
}
@comment{Proof that the splitting field of the $n'th$ iterate is
as large as possible (i.e., the full wreath product) for 
all $n\le 5\cdot10^7$.}

@comment{--DDD-- }

@article {MR1778843,
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@comment{\url{ArXiv:math.DS/0412438}}
 
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@comment{\url{ArXiv:math.DS/0403078}}

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@comment{UPDATE}
@misc {arxivNT0605724,
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          on special values of {H}asse-{W}eil zeta functions},
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  MRNUMBER = {MR2220105 (2007b:37010)},
MRREVIEWER = {Thomas Ward},
}
@comment{Includes p-adic analogues of multivariable Mahler measures.}

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@comment{UPDATE}
@misc {arxiv0909.4130,
    AUTHOR = {Diao, Hansheng and Silva, Cesar},
    TITLE = {Digraph Representations Of Rational Functions 
         Over $p$-adic Numbers },
     YEAR = {2009},
     NOTE = {\url{arXiv:0909.4130}},
}

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@book{devaney:dynamicsbook, 
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}

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@comment{--EEE-- }

@article {MR2079832,
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  MRNUMBER = {MR2079832},
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@incollection {MR2044517,
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@article {MR1876275,
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@misc {elkies:lowhtpts,
   AUTHOR = {Elkies, Noam},
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}

@comment{UPDATE}
@misc {arxiv0910.5704,
    AUTHOR = {Elsawy, Ahmed Noubi},
    TITLE = {Generalization of Some Arithmetical Properties of
        {F}ermat--{E}uler Dynamical Systems},
     YEAR = {2009},
     NOTE = {\url{arXiv:0910.5704}},
}

@incollection {MR1084181,
    AUTHOR = {Erd{\H{o}}s, P. and Granville, A. and Pomerance, C. and Spiro,
              C.},
     TITLE = {On the normal behavior of the iterates of some arithmetic
              functions},
 BOOKTITLE = {Analytic number theory (Allerton Park, IL, 1989)},
    SERIES = {Progr. Math.},
    VOLUME = {85},
     PAGES = {165--204},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1990},
   MRCLASS = {11N64},
  MRNUMBER = {MR1084181 (92a:11113)},
MRREVIEWER = {Tian Xin Cai},
}

@article {MR1027462,
    AUTHOR = {Er{\"e}menko, A. {\`E}.},
     TITLE = {Some functional equations connected with the iteration of
              rational functions},
   JOURNAL = {Algebra i Analiz},
  FJOURNAL = {Algebra i Analiz},
    VOLUME = {1},
      YEAR = {1989},
    NUMBER = {4},
     PAGES = {102--116},
      ISSN = {0234-0852},
   MRCLASS = {30D05 (34C35 39B20 58F08 58F11)},
  MRNUMBER = {MR1027462 (90m:30030)},
MRREVIEWER = {Peter M. Makienko},
}

@article {MR1783650,
    AUTHOR = {Everest, Graham and Pinner, Chris},
     TITLE = {Corrigendum: ``{B}ounding the elliptic {M}ahler measure.
              {II}'' [{J}. {L}ondon {M}ath. {S}oc. (2) \textbf{58} (1998), no.
              1, 1--8.]},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {62},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {640},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11G50 (11G05 11R09)},
  MRNUMBER = {MR1783650 (2001g:11103)},
MRREVIEWER = {Yann Bugeaud},
}
@article {MR1666050,
    AUTHOR = {Everest, Graham and Pinner, Chris},
     TITLE = {Bounding the elliptic {M}ahler measure. {II}},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {58},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {1--8},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11G50 (11G05 11R09)},
  MRNUMBER = {MR1666050 (2000a:11099)},
MRREVIEWER = {Yann Bugeaud},
}
@article {MR1373343,
    AUTHOR = {Everest, Graham and Fhlath{\'u}in, Br{\'{\i}}d N\'\i},
     TITLE = {The elliptic {M}ahler measure},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {120},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {13--25},
      ISSN = {0305-0041},
     CODEN = {MPCPCO},
   MRCLASS = {11G05 (11C08 11J99)},
  MRNUMBER = {MR1373343 (97e:11064)},
MRREVIEWER = {Gregory S. Call},
}
@article {everest:ellipticjensen,
   AUTHOR = {Everest, Graham},
    TITLE = {On the elliptic analogue of {J}ensen's formula},
  JOURNAL = {J. London Math. Soc. (2)},
 FJOURNAL = {The Journal of the London Mathematical Society. Second Series},
   VOLUME = {59},
     YEAR = {1999},
   NUMBER = {1},
    PAGES = {21--36},
}
@book {everestward:dynamicsbook,
   AUTHOR = {Everest, Graham and Ward, Thomas},
    TITLE = {Heights of polynomials and entropy in algebraic dynamics},
PUBLISHER = {Springer-Verlag London Ltd.},
  ADDRESS = {London},
     YEAR = {1999},
    PAGES = {xii+211},
}

@comment{UPDATE}
@misc{math.DS/0705.1067,
    title = {Dirichlet series for finite combinatorial rank dynamics}, 
    author = {Everest, G. and Miles, R. and Stevens, S. and Ward, T.},
    note = {\url{arXiv:0705.1067v1}}
}
@article {everestward:dynamicalheight,
   AUTHOR = {Everest, Graham and Ward, Thomas},
    TITLE = {A dynamical interpretation of the global canonical height on an
             elliptic curve},
  JOURNAL = {Experiment. Math.},
 FJOURNAL = {Experimental Mathematics},
   VOLUME = {7},
     YEAR = {1998},
   NUMBER = {4},
    PAGES = {305--316},
}

@article {MR1938222,
    AUTHOR = {Everest, Graham and van der Poorten, Alf and Puri, Yash
              and Ward, Thomas},
     TITLE = {Integer sequences and periodic points},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {5},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {Article 02.2.3, 10 pp. (electronic)},
      ISSN = {1530-7638},
   MRCLASS = {11B37 (11B68 37B10 39A10)},
  MRNUMBER = {MR1938222 (2003j:11014)},
MRREVIEWER = {Ali Messaoudi},
}
@book {MR1990179,
    AUTHOR = {Everest, Graham and van der Poorten, Alf and Shparlinski, Igor
              and Ward, Thomas},
     TITLE = {Recurrence {S}equences},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {104},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2003},
     PAGES = {xiv+318},
      ISBN = {0-8218-3387-1},
   MRCLASS = {11B37 (11B85 11G05 11J71 11K45 11T23 37B15 94A60)},
  MRNUMBER = {MR1990179 (2004c:11015)},
MRREVIEWER = {Yann Bugeaud},
}


@comment{--FFF-- }

@comment{UPDATE}
@misc {arxiv:0801.4811,
    AUTHOR = {Faber, Xander},
    TITLE = {Equidistribution of Dynamically Small Subvarieties 
              over the Function Field of a Curve},
     YEAR = {2008},
     NOTE = {\url{arXiv:0801.4811}},
}
@comment{UPDATE}
@misc {arxiv0907.4365,
    AUTHOR = {Faber, Xander},
    TITLE = {A Remark on the Effective Mordell Conjecture and Rational
         Pre-Images under Quadratic Dynamical Systems},
     YEAR = {2009},
     NOTE = {\url{arXiv:0907.4365}},
}
@comment{UPDATE}
@misc {arxiv0903.1344,
    AUTHOR = {Faber, Xander and Granville, Andrew},
    TITLE = {Prime Factors of Dynamical Sequences},
     YEAR = {2009},
     NOTE = {\url{arXiv:0903.1344}},
}

@comment{UPDATE}
@misc {arxiv:0810.1715,
    AUTHOR = {Faber, Xander and Hutz, Benjamin},
    TITLE = {On the Number of Rational Iterated Pre-images of 
                 the Origin Under Quadratic Dynamical Systems},
     YEAR = {2008},
     NOTE = {\url{arXiv:0810.1715}},
}

@article {arxiv:0805.0441,
    AUTHOR = {Faber, Xander and Hutz, Benjamin and Ingram, Patrick and
              Jones, Rafe and Manes, Michelle and Tucker, Thomas J. and
              Zieve, Michael E.},
     TITLE = {Uniform bounds on pre-images under quadratic dynamical
              systems},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {16},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {87--101},
      ISSN = {1073-2780},
   MRCLASS = {14G25 (11G18 14G05 37Bxx 37Fxx)},
  MRNUMBER = {MR2480563},
}

@article {MR1707699,
    AUTHOR = {Fagella, N{\'u}ria and Llibre, Jaume},
     TITLE = {Periodic points of holomorphic maps via {L}efschetz numbers},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {352},
      YEAR = {2000},
    NUMBER = {10},
     PAGES = {4711--4730},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {55M20 (37F10)},
  MRNUMBER = {MR1707699 (2001b:55003)},
MRREVIEWER = {Evelyn L. Hart},
}

@article {MR1995861,
    AUTHOR = {Fakhruddin, Najmuddin},
     TITLE = {Questions on self maps of algebraic varieties},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {18},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {109--122},
      ISSN = {0970-1249},
   MRCLASS = {14G05 (37A45)},
  MRNUMBER = {MR1995861 (2004f:14038)},
MRREVIEWER = {Yuri Tschinkel},
}
@article {MR1836365,
    AUTHOR = {Fakhruddin, Najmuddin},
     TITLE = {Boundedness results for periodic points on algebraic
              varieties},
   JOURNAL = {Proc. Indian Acad. Sci. Math. Sci.},
  FJOURNAL = {Indian Academy of Sciences. Proceedings. Mathematical
              Sciences},
    VOLUME = {111},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {173--178},
      ISSN = {0253-4142},
   MRCLASS = {11G35 (11G20 14G20 14G25)},
  MRNUMBER = {MR1836365 (2003a:11075)},
MRREVIEWER = {Atsushi Moriwaki},
}
@incollection {MR861971,
    AUTHOR = {Faltings, Gerd},
     TITLE = {Finiteness theorems for abelian varieties over number fields},
 BOOKTITLE = {Arithmetic geometry \textup{(}Storrs, Conn., 1984\textup{)}},
     PAGES = {9--27},
      NOTE = {Translated from the German original [Invent.\ Math.\ \textbf{73}
              (1983), no.\ 3, 349--366; ibid.\ \textbf{75} (1984), no.\ 2, 381]
              by Edward Shipz},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {1986},
   MRCLASS = {11G10 (14K15)},
  MRNUMBER = {MR861971},
}

@article {MR718935,
    AUTHOR = {Faltings, Gerd},
     TITLE = {Endlichkeitss\"atze f\"ur abelsche {V}ariet\"aten \"uber
              {Z}ahlk\"orpern},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {73},
      YEAR = {1983},
    NUMBER = {3},
     PAGES = {349--366},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11D41 (11G30 14G25)},
  MRNUMBER = {MR718935 (85g:11026a)},
MRREVIEWER = {James Milne},
}

@article {faltings:mordelllangconj,
    AUTHOR = {Faltings, Gerd},
     TITLE = {Diophantine approximation on abelian varieties},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {133},
      YEAR = {1991},
     PAGES = {349--366},
}

@article {fatou:1919,
    AUTHOR = {Fatou, P.},
     TITLE = {Sur les {\'e}quations fonctionnelles},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {47},
      YEAR = {1919},
     PAGES = {161--271},
}
@article {fatou:1920,
    AUTHOR = {Fatou, P.},
     TITLE = {Sur les {\'e}quations fonctionnelles},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {48},
      YEAR = {1920},
     PAGES = {33--94 and 208--314},
}


@article {MR2092012,
    AUTHOR = {Favre, Charles and Rivera-Letelier, Juan},
     TITLE = {Th\'eor\`eme d'\'equidistribution de {B}rolin en dynamique
              {$p$}-adique},
   JOURNAL = {C.~R.~Math. Acad. Sci. Paris},
  FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
    VOLUME = {339},
      YEAR = {2004},
    NUMBER = {4},
     PAGES = {271--276},
      ISSN = {1631-073X},
   MRCLASS = {37F10 (11S85)},
  MRNUMBER = {MR2092012},
}

@article {arxiv0407471,
    AUTHOR = {Favre, Charles and Rivera-Letelier, Juan},
     TITLE = {\'{E}quidistribution quantitative des points de petite hauteur
              sur la droite projective},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {335},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {311--361},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11G50 (37F10)},
  MRNUMBER = {MR2221116},
      NOTE = {Corrigendum: Math. Ann. 339 (2007), 799--801},
}

@misc {arxiv0503720,
    AUTHOR = {Fernandez, Gabriela},
    TITLE = {Wandering {F}atou components on {$p$}-adic polynomial dynamics},
     YEAR = {2004},
     NOTE = {\url{ArXiv:math.DS/0503720}},
}
@comment{Rivera-Letelier notes: Fernandez shows that Benedetto's
examples are dense in an open subset of the space of polynomials over
$C_p$ of a given degree $\ge p + 1$.}

@article {flynnetal:cyclesofquads,
   AUTHOR = {Flynn, E. V. and Poonen, Bjorn and Schaefer, Edward F.},
    TITLE = {Cycles of quadratic polynomials and rational points on a
             genus-$2$ curve},
  JOURNAL = {Duke Math. J.},
 FJOURNAL = {Duke Mathematical Journal},
   VOLUME = {90},
     YEAR = {1997},
   NUMBER = {3},
    PAGES = {435--463},
}

@incollection {MR1332961,
    AUTHOR = {Forn{\ae}ss, John Erik and Sibony, Nessim},
     TITLE = {Complex dynamics in higher dimensions},
 BOOKTITLE = {Complex {P}otential {T}heory (Montreal, PQ, 1993)},
    SERIES = {NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.},
    VOLUME = {439},
     PAGES = {131--186},
 PUBLISHER = {Kluwer Acad. Publ.},
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      YEAR = {1994},
   MRCLASS = {32H50 (58F23)},
  MRNUMBER = {MR1332961 (96k:32057)},
MRREVIEWER = {Eric Bedford},
}

@article {MR1285389,
    AUTHOR = {Forn{\ae}ss, John Erik and Sibony, Nessim},
     TITLE = {Complex dynamics in higher dimension. {I}},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
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      YEAR = {1994},
     PAGES = {5, 201--231},
      ISSN = {0303-1179},
   MRCLASS = {32H50 (32H20 58F23)},
  MRNUMBER = {MR1285389 (95i:32036)},
MRREVIEWER = {Serguei M. Voronin},
}

@incollection {MR1369137,
    AUTHOR = {Fornaess, John Erik and Sibony, Nessim},
     TITLE = {Complex dynamics in higher dimension. {II}},
 BOOKTITLE = {Modern {M}ethods in {C}omplex {A}nalysis (Princeton, NJ, 1992)},
    SERIES = {Ann. of Math. Stud.},
    VOLUME = {137},
     PAGES = {135--182},
 PUBLISHER = {Princeton Univ. Press},
   ADDRESS = {Princeton, NJ},
      YEAR = {1995},
   MRCLASS = {32H50 (32C30 58F23)},
  MRNUMBER = {MR1369137 (97g:32033)},
MRREVIEWER = {Eric Bedford},
}
@book {MR2014891,
    AUTHOR = {Fresnel, Jean and van der Put, Marius},
     TITLE = {Rigid analytic geometry and its applications},
    SERIES = {Progress in Mathematics},
    VOLUME = {218},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {2004},
     PAGES = {xii+296},
      ISBN = {0-8176-4206-4},
   MRCLASS = {14G22 (30G06 30H05 32P05)},
  MRNUMBER = {MR2014891 (2004i:14023)},
MRREVIEWER = {Lorenzo Ramero},
}
@article {MR991490,
    AUTHOR = {Friedland, Shmuel and Milnor, John},
     TITLE = {Dynamical properties of plane polynomial automorphisms},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {9},
      YEAR = {1989},
    NUMBER = {1},
     PAGES = {67--99},
      ISSN = {0143-3857},
   MRCLASS = {58F99},
  MRNUMBER = {MR991490 (90f:58163)},
MRREVIEWER = {M. Lyubich},
}

@comment{--GGG-- }

@article {MR1363145,
    AUTHOR = {Gallas, Jason A. C.},
     TITLE = {Units: remarkable points in dynamical systems},
   JOURNAL = {Phys. A},
  FJOURNAL = {Physica A. Statistical and Theoretical Physics},
    VOLUME = {222},
      YEAR = {1995},
    NUMBER = {1-4},
     PAGES = {125--151},
      ISSN = {0378-4371},
     CODEN = {PHYSAG},
   MRCLASS = {58F20 (11R27 58F08)},
  MRNUMBER = {MR1363145 (96m:58205)},
MRREVIEWER = {J. C. Lagarias},
}
@comment{The author studies the units in the moduli space of Henon maps}

@book {MR785216,
       KEY = {Geometry of K3 surfaces},
     TITLE = {G\'eom\'etrie des surfaces {$K3$}: modules et p\'eriodes},
      NOTE = {Papers from the seminar held in Palaiseau, October
              1981--January 1982,
              Ast\'erisque No. 126 (1985)},
 PUBLISHER = {Soci\'et\'e Math\'ematique de France},
   ADDRESS = {Paris},
      YEAR = {1985},
     PAGES = {1--193},
      ISSN = {0303-1179},
   MRCLASS = {32J15 (14J25 14J28 53C25)},
  MRNUMBER = {MR785216 (87h:32052)},
MRREVIEWER = {Werner Kleinert},
}

@phdthesis{getachew:thesis, 
   AUTHOR = {Getachew, Selemon},
    TITLE = {Galois Theory of Polynomial Iterates},
   SCHOOL = {Brown University},
     YEAR = {2000}
	}
@article {MR2255176,
    AUTHOR = {Ghioca, Dragos},
     TITLE = {Equidistribution for torsion points of a {D}rinfeld module},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {336},
      YEAR = {2006},
    NUMBER = {4},
     PAGES = {841--865},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11G09 (11G50)},
  MRNUMBER = {MR2255176},
}

@article {arXiv:0704.1333,
    AUTHOR = {Ghioca, D. and Tucker, T. J.},
     TITLE = {A dynamical version of the {M}ordell-{L}ang conjecture for the
              additive group},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {144},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {304--316},
      ISSN = {0010-437X},
   MRCLASS = {11G09 (14K12 37F10)},
  MRNUMBER = {MR2406114 (2009c:11086)},
MRREVIEWER = {Liang-Chung Hsia},
}

@article {arxivNT0609120,
    AUTHOR = {Ghioca, D. and Tucker, T. J.},
     TITLE = {Equidistribution and integral points for {D}rinfeld modules},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {360},
      YEAR = {2008},
    NUMBER = {9},
     PAGES = {4863--4887},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {11G50 (11G09 11J93)},
  MRNUMBER = {MR2403707 (2009c:11095)},
MRREVIEWER = {Lenny Fukshansky},
}


@comment{UPDATE}
@misc {arXiv:0705.4047,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas},
    TITLE = {$p$-adic logarithms for polynomial dynamics},
     YEAR = {2007},
     NOTE = {\url{arXiv:0705.4047}},
}
@comment{UPDATE}
@misc {arxiv0710.1669,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas},
    TITLE = {Mordell--{L}ang and {S}kolem--{M}ahler--{L}ech theorems 
               for endomorphisms of semiabelian varieties},
     YEAR = {2007},
     NOTE = {\url{arXiv:0710.1669}},
}

@comment{UPDATE}
@article {arxiv0805.1560,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas},
    TITLE = {Periodic points, linearizing maps, and the 
            dynamical {M}ordell--{L}ang problem},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {129},
      YEAR = {2009},
    NUMBER = {6},
     PAGES = {1392--1403},
}

@comment{UPDATE}
@misc {arxiv:0808.3263,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas},
    TITLE = {Proof of a dynamical {B}ogomolov conjecture for 
                lines under polynomial actions},
     YEAR = {2008},
     NOTE = {\url{arXiv:0808.3263}},
}

@article {arxiv0705.1954,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas J. and Zieve, Michael E.},
     TITLE = {Intersections of polynomials orbits, and a dynamical
              {M}ordell-{L}ang conjecture},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {171},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {463--483},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {37F10 (11C08 14G99)},
  MRNUMBER = {MR2367026 (2008k:37099)},
MRREVIEWER = {Joseph H. Silverman},
}

@comment{UPDATE}
@misc {arxiv0807.3576,
    AUTHOR = {Ghioca, Dragos and Tucker, Thomas and Zieve, Michael},
    TITLE = {Linear relations between polynomial orbits},
     YEAR = {2008},
     NOTE = {\url{arXiv:0807.3576}},
}
@comment{UPDATE}
@misc {arxiv0908.3920,
    AUTHOR = {Glebsky, Lev and Shparlinski, Igor},
    TITLE = {Short Cycles in Repeated Exponentiation Modulo a Prime},
     YEAR = {2009},
     NOTE = {\url{arXiv:0908.3920}},
}
@incollection {arxivFA0602081,
    AUTHOR = {Gl{\"o}ckner, Helge},
     TITLE = {Aspects of {$p$}-adic non-linear functional analysis},
 BOOKTITLE = {$p$-adic mathematical physics},
    SERIES = {AIP Conf. Proc.},
    VOLUME = {826},
     PAGES = {237--253},
 PUBLISHER = {Amer. Inst. Phys.},
   ADDRESS = {Melville, NY},
      YEAR = {2006},
   MRCLASS = {46S10 (47S10)},
  MRNUMBER = {MR2258689},
}
@comment{\url{ArXiv:math.FA/0602081}}

@article {arxiv0610497,
    AUTHOR = {Gorodnik, Alexander and Oh, Hee and Shah, Nimish},
     TITLE = {Integral points on symmetric varieties and {S}atake
              compactifications},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {131},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {1--57},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {22Exx (14Gxx)},
  MRNUMBER = {MR2488484},
}

@book {MR1488696,
    AUTHOR = {Gouv{\^e}a, Fernando Q.},
     TITLE = {{$p$}-adic numbers},
    SERIES = {Universitext},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1997},
     PAGES = {vi+298},
      ISBN = {3-540-62911-4},
   MRCLASS = {11S80 (11-01 12J25)},
  MRNUMBER = {MR1488696 (98h:11155)},
}

@book {MR1397498,
    AUTHOR = {Graham, Ronald L. and Knuth, Donald E. and Patashnik, Oren},
     TITLE = {Concrete {M}athematics},
   EDITION = {Second},
 PUBLISHER = {Addison-Wesley Publishing Company},
   ADDRESS = {Reading, MA},
      YEAR = {1994},
     PAGES = {xiv+657},
      ISBN = {0-201-55802-5},
   MRCLASS = {68-01 (00-01 00A05 05-01 68Rxx)},
  MRNUMBER = {MR1397498 (97d:68003)},
MRREVIEWER = {Volker Strehl},
}
@article {greenmatigon:padicdisk,
   AUTHOR = {Green, Barry and Matignon, Michel},
    TITLE = {Order $p$ automorphisms of the open disc of a $p$-adic field},
  JOURNAL = {J. Amer. Math. Soc.},
 FJOURNAL = {Journal of the American Mathematical Society},
   VOLUME = {12},
     YEAR = {1999},
   NUMBER = {1},
    PAGES = {269--303},
}

@book {MR1288523,
    AUTHOR = {Griffiths, Phillip and Harris, Joseph},
     TITLE = {Principles of {A}lgebraic {G}eometry},
    SERIES = {Wiley Classics Library},
      NOTE = {Reprint of the 1978 original},
 PUBLISHER = {John Wiley \& Sons Inc.},
   ADDRESS = {New York},
      YEAR = {1994},
     PAGES = {xiv+813},
      ISBN = {0-471-05059-8},
   MRCLASS = {14-01},
  MRNUMBER = {MR1288523 (95d:14001)},
}

@article {arxiv0801.4508,
    AUTHOR = {Gubler, Walter},
     TITLE = {Equidistribution over function fields},
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {127},
      YEAR = {2008},
    NUMBER = {4},
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      ISSN = {0025-2611},
     CODEN = {MSMHB2},
   MRCLASS = {14G40 (11G50)},
  MRNUMBER = {MR2457191},
}


@article {MR1948064,
    AUTHOR = {Guedj, Vincent and Sibony, Nessim},
     TITLE = {Dynamics of polynomial automorphisms of {$\mathbb{C}\sp k$}},
   JOURNAL = {Ark. Mat.},
  FJOURNAL = {Arkiv f\"or Matematik},
    VOLUME = {40},
      YEAR = {2002},
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      ISSN = {0004-2080},
     CODEN = {AKMTAJ},
   MRCLASS = {32H50 (37F10)},
  MRNUMBER = {MR1948064 (2004b:32029)},
MRREVIEWER = {Christian P. Wolf},
}

@incollection {MR1838286,
    AUTHOR = {Gundlach, Matthias and Khrennikov, Andrei and Lindahl,
              Karl-Olof},
     TITLE = {Topological transitivity for {$p$}-adic dynamical systems},
 BOOKTITLE = {$p$-adic functional analysis (Ioannina, 2000)},
    SERIES = {Lecture Notes in Pure and Appl. Math.},
    VOLUME = {222},
     PAGES = {127--132},
 PUBLISHER = {Dekker},
   ADDRESS = {New York},
      YEAR = {2001},
   MRCLASS = {37A45 (11S99 37A05 37B05 37E99)},
  MRNUMBER = {MR1838286 (2002d:37014)},
MRREVIEWER = {Anatoly N. Kochubei},
}
@article {MR1876486,
    AUTHOR = {Gundlach, Matthias and Khrennikov, Andrei and Lindahl,
              Karl-Olof},
     TITLE = {On ergodic behavior of {$p$}-adic dynamical systems},
   JOURNAL = {Infin. Dimens. Anal. Quantum Probab. Relat. Top.},
  FJOURNAL = {Infinite Dimensional Analysis, Quantum Probability and Related
              Topics},
    VOLUME = {4},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {569--577},
      ISSN = {0219-0257},
   MRCLASS = {37A45 (11S05 37E99 37F99)},
  MRNUMBER = {MR1876486 (2002j:37015)},
MRREVIEWER = {Manfred Einsiedler},
}


@article {MR0437489,
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     TITLE = {Sur les polyn\^omes \`a coefficients entiers et de
              discriminant donn\'e},
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  FJOURNAL = {Polska Akademia Nauk. Instytut Matematyczny. Acta Arithmetica},
    VOLUME = {23},
      YEAR = {1973},
     PAGES = {419--426},
      ISSN = {0065-1036},
   MRCLASS = {12A20},
  MRNUMBER = {MR0437489 (55 \#10419a)},
MRREVIEWER = {Maurice Mignotte},
}

@article {MR0437490,
    AUTHOR = {Gy{\H{o}}ry, K.},
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   JOURNAL = {Publ. Math. Debrecen},
  FJOURNAL = {Publicationes Mathematicae Debrecen},
    VOLUME = {21},
      YEAR = {1974},
     PAGES = {125--144},
      ISSN = {0033-3883},
   MRCLASS = {12A20},
  MRNUMBER = {MR0437490 (55 \#10419b)},
MRREVIEWER = {Maurice Mignotte},
}

@article {MR0437491,
    AUTHOR = {Gy{\H{o}}ry, K.},
     TITLE = {Sur les polyn\^omes \`a coefficients entiers et de
              discriminant donn\'e. {III}},
   JOURNAL = {Publ. Math. Debrecen},
  FJOURNAL = {Publicationes Mathematicae Debrecen},
    VOLUME = {23},
      YEAR = {1976},
    NUMBER = {1-2},
     PAGES = {141--165},
      ISSN = {0033-3883},
   MRCLASS = {12A20},
  MRNUMBER = {MR0437491 (55 \#10419c)},
MRREVIEWER = {Maurice Mignotte},
}

@comment{--HHH-- }

@book {MR1088254,
    AUTHOR = {Haaser, Norman B. and Sullivan, Joseph A.},
     TITLE = {Real {A}nalysis},
      NOTE = {Revised reprint of the 1971 original},
 PUBLISHER = {Dover Publications Inc.},
   ADDRESS = {New York},
      YEAR = {1991},
     PAGES = {x+341},
      ISBN = {0-486-66509-7},
   MRCLASS = {00A05 (26-01 28-01 46-01)},
  MRNUMBER = {MR1088254 (92a:00006)},
}

@article {MR1963443,
    AUTHOR = {Halter-Koch, F. and Kone{\v{c}}n{\'a}, P.},
     TITLE = {Polynomial cycles in finite extension fields},
   JOURNAL = {Math. Slovaca},
  FJOURNAL = {Mathematica Slovaca},
    VOLUME = {52},
      YEAR = {2002},
    NUMBER = {5},
     PAGES = {531--535},
      ISSN = {0139-9918},
   MRCLASS = {11C08 (11T06)},
  MRNUMBER = {MR1963443 (2003m:11047)},
MRREVIEWER = {W. Narkiewicz},
}

@article {MR2001h:11028,
    AUTHOR = {Halter-Koch, F. and Narkiewicz, W.},
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    VOLUME = {56},
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    NUMBER = {3-4},
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  MRNUMBER = {2001h:11028},
MRREVIEWER = {Liang-Chung Hsia},
}

@incollection {kochnarkdynunits97,
    AUTHOR = {Halter-Koch, F. and Narkiewicz, W.},
     TITLE = {Polynomial cycles and dynamical units},
 BOOKTITLE = {Proceedings of a Conference on 
              Analytic and Elementary Number Theory (Wien 1996)},
     PAGES = {70--80},
      YEAR = {1997},
      NOTE = {\url{www.boku.ac.at/math/proc.html}},
}

@article {MR94j:14016,
    AUTHOR = {Halter-Koch, F. and Narkiewicz, W.},
     TITLE = {Finiteness properties of polynomial mappings},
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    VOLUME = {159},
      YEAR = {1992},
     PAGES = {7--18},
      ISSN = {0025-584X},
     CODEN = {MTMNAQ},
   MRCLASS = {14E05 (12F20)},
  MRNUMBER = {94j:14016},
MRREVIEWER = {Gary H. Meisters},
}

@article {MR1328818,
    AUTHOR = {Halter-Koch, F. and Narkiewicz, W.},
     TITLE = {Polynomial cycles in finitely generated domains},
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  FJOURNAL = {Monatshefte f\"ur Mathematik},
    VOLUME = {119},
      YEAR = {1995},
    NUMBER = {4},
     PAGES = {275--279},
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     CODEN = {MNMTA2},
   MRCLASS = {13G05 (13B25 14E05)},
  MRNUMBER = {MR1328818 (96d:13035)},
MRREVIEWER = {Jean-Luc Chabert},
}

@article {MR0119227,
    AUTHOR = {Harris, Bernard},
     TITLE = {Probability distributions related to random mappings},
   JOURNAL = {Ann. Math. Statist.},
    VOLUME = {31},
      YEAR = {1960},
     PAGES = {1045--1062},
   MRCLASS = {60.00 (05.00)},
  MRNUMBER = {MR0119227 (22 \#9993)},
MRREVIEWER = {J. Riordan},
}

@book {MR1416564,
    AUTHOR = {Harris, Joseph},
     TITLE = {Algebraic {G}eometry},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {133},
      NOTE = {Corrected reprint of the 1992 original},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1995},
     PAGES = {xx+328},
      ISBN = {0-387-97716-3},
   MRCLASS = {14-01},
  MRNUMBER = {MR1416564 (97e:14001)},
}

@book {hartshorne, 
    AUTHOR = {Hartshorne, Robin},
     TITLE = {Algebraic {G}eometry},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {52},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1977},
     PAGES = {xvi+496},
      ISBN = {0-387-90244-9},
   MRCLASS = {14-01},
  MRNUMBER = {MR0463157 (57 \#3116)},
MRREVIEWER = {Robert Speiser},
}


@article {arxiv0604521,
    AUTHOR = {Hasselblatt, Boris and Propp, James},
     TITLE = {Degree-growth of monomial maps},
   JOURNAL = {Ergodic Theory Dynam. Systems},
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    VOLUME = {27},
      YEAR = {2007},
    NUMBER = {5},
     PAGES = {1375--1397},
      ISSN = {0143-3857},
   MRCLASS = {37F45 (32H50 37B40)},
  MRNUMBER = {MR2358970 (2008k:37104a)},
MRREVIEWER = {Mattias Jonsson},
      NOTE = {Corrigendum Ergodic Theory Dynam. 
                   Systems 27 (2007), no. 6, 1999},
}

@article {MR0422932,
    AUTHOR = {H{\'e}non, M.},
     TITLE = {A two-dimensional mapping with a strange attractor},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {50},
      YEAR = {1976},
    NUMBER = {1},
     PAGES = {69--77},
      ISSN = {0010-3616},
   MRCLASS = {40A05},
  MRNUMBER = {MR0422932 (54 \#10917)},
MRREVIEWER = {P. Fischer},
}

@inproceedings{hermanyoccoz:nonarchdynamics, 
   AUTHOR = {M. Herman and J.-C. Yoccoz},
    TITLE = {Generalizations of some theorems of small divisors to non-Archimedean fields},
BOOKTITLE = {Geometric Dynamics},
     YEAR = {1983},
    PAGES = {408--447},
 PUBLISHER = {Springer-Verlag},
   SERIES = {Lecture Notes in Mathematics},
   VOLUME = {1007},
     NOTE = {Rio de Janairo (1981)}
}

@book {hindrysilverman:diophantinegeometry,
    AUTHOR = {Hindry, Marc and Silverman, Joseph H.},
     TITLE = {Diophantine {G}eometry: An {I}ntroduction},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {201},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2000},
     PAGES = {xiv+558},
      ISBN = {0-387-98975-7; 0-387-98981-1},
   MRCLASS = {11Gxx (11-02 11G10 11G30 11G50 14G25)},
  MRNUMBER = {MR1745599 (2001e:11058)},
MRREVIEWER = {Dino J. Lorenzini},
}

@article {hindrysilverman:integralpts,
    AUTHOR = {Hindry, Marc and Silverman, Joseph H.},
     TITLE = {The canonical height and integral points on elliptic curves},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {93},
      YEAR = {1988},
    NUMBER = {2},
     PAGES = {419--450},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G05 (11D25 14G25)},
  MRNUMBER = {MR948108 (89k:11044)},
MRREVIEWER = {Ernst-Ulrich Gekeler},
}

@article {hindrysilverman:torsionpoints,
    AUTHOR = {Hindry, Marc and Silverman, Joseph H.},
     TITLE = {Sur le nombre de points de torsion rationnels sur une courbe
              elliptique},
   JOURNAL = {C.~R.~Acad. Sci. Paris S\'er. I Math.},
  FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
              Math\'ematique},
    VOLUME = {329},
      YEAR = {1999},
    NUMBER = {2},
     PAGES = {97--100},
      ISSN = {0764-4442},
     CODEN = {CASMEI},
   MRCLASS = {11G05 (11G50 14G05)},
  MRNUMBER = {MR1710502 (2000g:11047)},
MRREVIEWER = {Carlo Gasbarri},
}

@incollection {hindrysilverman:lehmer, 
    AUTHOR = {Hindry, Marc and Silverman, Joseph H.},
     TITLE = {On {L}ehmer's conjecture for elliptic curves},
 BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, Paris 1988--1989},
    SERIES = {Progr. Math.},
    VOLUME = {91},
     PAGES = {103--116},
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   ADDRESS = {Boston, MA},
      YEAR = {1990},
   MRCLASS = {11G05 (14G25)},
  MRNUMBER = {MR1104702 (92e:11062)},
MRREVIEWER = {Philippe Satg{\'e}},
}

@article {hsia:weakneronmodel,
    AUTHOR = {Hsia, Liang-Chung},
     TITLE = {A weak {N}\'eron model with applications to {$p$}-adic
              dynamical systems},
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  FJOURNAL = {Compositio Mathematica},
    VOLUME = {100},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {277--304},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {14G20 (14E99)},
  MRNUMBER = {MR1387667 (97j:14024)},
MRREVIEWER = {Guido Van Steen},
}

@article {hsia:periodicpoint,
    AUTHOR = {Hsia, Liang-Chung},
     TITLE = {Closure of periodic points over a non-{A}rchimedean field},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {62},
      YEAR = {2000},
    NUMBER = {3},
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      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11S80 (37F10 37F50)},
  MRNUMBER = {MR1794277 (2001j:11117)},
MRREVIEWER = {Michael E. Zieve},
}

@article {hsia:dynamicalzeta,
    AUTHOR = {Hsia, Liang-Chung},
     TITLE = {On the dynamical height zeta functions},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {63},
      YEAR = {1997},
    NUMBER = {1},
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      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G30 (11M45 14G10)},
  MRNUMBER = {MR1438655 (99c:11076)},
MRREVIEWER = {Emmanuel Peyre},
}

@UNPUBLISHED{hsia:padicequidist,
   AUTHOR  = {Hsia, Liang-Chung},
   TITLE   = {$p$-adic equidistribution theorems},
   NOTE    = {manuscript},
   YEAR    = {2003},
}

@article {hsia:drinfeld,
    AUTHOR = {Hsia, Liang-Chung},
     TITLE = {On the reduction of a non-torsion point of a {D}rinfeld
              module},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {128},
      YEAR = {2008},
    NUMBER = {6},
     PAGES = {1458--1484},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G09},
  MRNUMBER = {MR2419173 (2009f:11065)},
MRREVIEWER = {Ambrus P{\'a}l},
}

@comment{UPDATE}
@misc {arxiv:0801.3045,
    AUTHOR = {Hsia, Liang-Chung and Silverman, Joseph H.},
    TITLE = {On a Dynamical {B}rauer--{M}anin Obstruction},
     YEAR = {2008},
     NOTE = {\url{arXiv:0801.3045}},
}
@comment{UPDATE}
@misc {arxiv0910.4498,
    AUTHOR = {Hsia, Liang-Chung and Silverman, Joseph H.},
    TITLE = {A quantitative estimate for quasi-integral points in orbits},
     YEAR = {2009},
     NOTE = {\url{arXiv:0910.4498}},
}

@book {MR665428,
    AUTHOR = {Hua, Loo Keng},
     TITLE = {Introduction to {N}umber {T}heory},
      NOTE = {Translated from the Chinese by Peter Shiu},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1982},
     PAGES = {xviii+572},
      ISBN = {3-540-10818-1},
   MRCLASS = {10-01},
  MRNUMBER = {MR665428 (83f:10001)},
}

@incollection {hubbard:henonmap,
    AUTHOR = {Hubbard, John},
     TITLE = {The {H}\'enon mapping in the complex domain},
 BOOKTITLE = {Chaotic {D}ynamics and {F}ractals (Atlanta, Ga., 1985)},
    SERIES = {Notes Rep. Math. Sci. Engrg.},
    VOLUME = {2},
     PAGES = {101--111},
 PUBLISHER = {Academic Press},
   ADDRESS = {Orlando, FL},
      YEAR = {1986},
   MRCLASS = {58F11 (30D05)},
  MRNUMBER = {MR858009},
}

@article {MR1768111,
    AUTHOR = {Hubbard, John and Papadopol, Peter and Veselov, Vladimir},
     TITLE = {A compactification of {H}\'enon mappings in {$\mathbb{C}\sp 2$}
              as dynamical systems},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {184},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {203--270},
      ISSN = {0001-5962},
     CODEN = {ACMAA8},
   MRCLASS = {37F10 (32H50)},
  MRNUMBER = {MR1768111 (2001f:37056)},
MRREVIEWER = {Adrien Douady},
}

@incollection {MR1315537,
    AUTHOR = {Hubbard, John and Schleicher, Dierk},
     TITLE = {The spider algorithm},
 BOOKTITLE = {Complex {D}ynamical {S}ystems (Cincinnati, OH, 1994)},
    SERIES = {Proc. Sympos. Appl. Math.},
    VOLUME = {49},
     PAGES = {155--180},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1994},
   MRCLASS = {58F23 (30D05)},
  MRNUMBER = {MR1315537},
}

@phdthesis{hutz:thesis, 
    AUTHOR = {Hutz, Benjamin},
     TITLE = {Arithmetic Dynamics on Varieties in Dimension Greater Than One},
   SCHOOL = {Brown University},
     YEAR = {2007}
}
@comment{UPDATE}
@misc {arxiv:0801.3648,
    AUTHOR = {Hutz, Benjamin},
    TITLE = {A Computational Investigation of {W}ehler {K}3 Surfaces},
     YEAR = {2008},
     NOTE = {\url{arXiv:0801.3648}},
}
@comment{UPDATE}
@misc {arxiv:0801.3645,
    AUTHOR = {Hutz, Benjamin},
    TITLE = {Good Reduction of Periodic Points},
     YEAR = {2008},
     NOTE = {\url{arXiv:0801.3645}},
}
@comment{UPDATE}
@misc {arxiv:0801.3643,
    AUTHOR = {Hutz, Benjamin},
    TITLE = {Dynatomic cycles for morphisms of projective varieties},
     YEAR = {2008},
     NOTE = {\url{arXiv:0801.3643}},
}
@comment{UPDATE}
@misc {arxiv:0811.3225,
    AUTHOR = {Hutz, Benjamin},
    TITLE = {Rational Periodic Points for Degree Two Polynomial 
        Maps on Projective Space},
     YEAR = {2008},
     NOTE = {\url{arXiv:0811.3225}},
}

@misc {arxiv0909.5050,
    AUTHOR = {Hutz, Benjamin and Ingram, Patrick},
    TITLE = {Numerical Evidence for a Conjecture of Poonen},
     YEAR = {2009},
     NOTE = {\url{arXiv:0909.5050}},
}

@comment{--III-- }

@comment{UPDATE}
@misc {arxiv0805.1554,
    AUTHOR = {Ih, Su-Ion and Tucker, Thomas},
    TITLE = {A finiteness property for preperiodic points 
           of {C}hebyshev polynomials},
     YEAR = {2008},
     NOTE = {\url{arXiv:0805.1554}},
}

@comment{UPDATE}
@misc {arxiv0709.4154,
    AUTHOR = {Ingram, Patrick},
    TITLE = {Lower bounds on the canonical height associated 
             to the morphism $\phi(z)= z^d+c$},
     YEAR = {2007},
     NOTE = {\url{arxiv.org/abs/0709.4154}},
}
@article {arXiv:0707.2505,
    AUTHOR = {Ingram, Patrick and Silverman, Joseph H.},
     TITLE = {Primitive divisors in arithmetic dynamics},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {146},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {289--302},
      ISSN = {0305-0041},
     CODEN = {MPCPCO},
   MRCLASS = {11B37 (11A41 37Fxx)},
  MRNUMBER = {MR2475968},
}

@article {MR2076045,
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     TITLE = {Effective asymptotics for some nonlinear recurrences and
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   JOURNAL = {Acta Math. Univ. Comenian. (N.S.)},
  FJOURNAL = {Acta Mathematica Universitatis Comenianae. New Series},
    VOLUME = {73},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {75--87},
      ISSN = {0862-9544},
   MRCLASS = {11B37 (11B83 11K31)},
  MRNUMBER = {MR2076045 (2005f:11018)},
MRREVIEWER = {C{\'e}cile Dartyge},
}
@book {irelandrosen:gtm, 
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     TITLE = {A {C}lassical {I}ntroduction to {M}odern {N}umber {T}heory},
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    VOLUME = {84},
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 PUBLISHER = {Springer-Verlag},
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      YEAR = {1990},
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      ISBN = {0-387-97329-X},
   MRCLASS = {11-01 (11-02)},
  MRNUMBER = {MR1070716 (92e:11001)},
MRREVIEWER = {Glenn Stevens},
}

@comment{--JJJ-- }
@book {MR734483,
    AUTHOR = {J{\"a}nich, Klaus},
     TITLE = {Topology},
    SERIES = {Undergraduate Texts in Mathematics},
      NOTE = {With a chapter by Theodor Br\"ocker,
              Translated from the German by Silvio Levy},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1984},
     PAGES = {ix+192},
      ISBN = {0-387-90892-7},
   MRCLASS = {54-01 (55-01 57-01)},
  MRNUMBER = {MR734483 (85a:54001)},
}

@comment{UPDATE}
@misc {arXiv:0712.0963,
    AUTHOR = {Jenkins, Adrian and Spallone, Steven},
    TITLE = {A $p$-adic approach to local analytic dynamics: analytic flows and
              analytic maps tangent to the identity},
     YEAR = {2007},
     NOTE = {\url{arXiv:0712.0963}},
}

@article {MR2062277,
    AUTHOR = {Jogia, Danesh and Roberts, John A. G. and Vivaldi, Franco},
     TITLE = {The {H}asse-{W}eil bound and integrability detection in
              rational maps},
   JOURNAL = {J. Nonlinear Math. Phys.},
  FJOURNAL = {Journal of Nonlinear Mathematical Physics},
    VOLUME = {10},
      YEAR = {2003},
    NUMBER = {suppl. 2},
     PAGES = {166--180},
      ISSN = {1402-9251},
   MRCLASS = {37F99 (11Z05 37J10 37J35)},
  MRNUMBER = {MR2062277 (2005b:37099)},
}

@article {MR2200430,
    AUTHOR = {Jogia, Danesh and Roberts, John A. G. and Vivaldi, Franco},
     TITLE = {An algebraic geometric approach to integrable maps of the
              plane},
   JOURNAL = {J. Phys. A},
  FJOURNAL = {Journal of Physics. A. Mathematical and General},
    VOLUME = {39},
      YEAR = {2006},
    NUMBER = {5},
     PAGES = {1133--1149},
      ISSN = {0305-4470},
     CODEN = {JPHAC5},
   MRCLASS = {14H52 (11G05 37F99 37J35)},
  MRNUMBER = {MR2200430 (2006k:14055)},
MRREVIEWER = {Todor E. Milanov},
}

@phdthesis{jones:thesis, 
    AUTHOR = {Jones, Rafe},
     TITLE = {{G}alois {M}artingales and the {$p$}-adic {H}yperbolic
           {M}andelbrot {S}et},
   SCHOOL = {Brown University},
     YEAR = {2005}
}

@article {jones:itgaltow,
    AUTHOR = {Jones, Rafe},
     TITLE = {Iterated {G}alois towers, their associated martingales, and
              the {$p$}-adic {M}andelbrot set},
   JOURNAL = {Compos. Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {143},
      YEAR = {2007},
    NUMBER = {5},
     PAGES = {1108--1126},
      ISSN = {0010-437X},
   MRCLASS = {11R32 (37F45 60G42)},
  MRNUMBER = {MR2360312 (2008i:11131)},
MRREVIEWER = {Thomas Ward},
}

@article {jones:denprimdiv,
    AUTHOR = {Jones, Rafe},
     TITLE = {The density of prime divisors in the arithmetic dynamics of
              quadratic polynomials},
   JOURNAL = {J. Lond. Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {78},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {523--544},
      ISSN = {0024-6107},
   MRCLASS = {37Exx (11B37 60G42)},
  MRNUMBER = {MR2439638},
}

@comment{UPDATE}
@misc {arXiv:0706.2384,
    AUTHOR = {Jones, Rafe and Rouse, Jeremy},
    TITLE = {Iterated endomorphisms of Abelian algebraic groups},
     YEAR = {2007},
     NOTE = {\url{arXiv:0706.2384 }},
}

@article {julia:1918,
    AUTHOR = {Julia, G.},
     TITLE = {M\'emoire sur L'it\'eration des Fonctions Rationelles},
   JOURNAL = {Journal de Math. Pures et Appl.},
    VOLUME = {8},
      YEAR = {1918},
     PAGES = {47--245},
}

@article {MR1509242,
    AUTHOR = {Julia, Gaston},
     TITLE = {M\'emoire sur la permutabilit\'e des fractions rationnelles},
   JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (3)},
  FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
              Troisi\`eme S\'erie},
    VOLUME = {39},
      YEAR = {1922},
     PAGES = {131--215},
      ISSN = {0012-9593},
   MRCLASS = {Contributed Item},
  MRNUMBER = {MR1509242},
}

@comment{--KKK-- }

@article {MR1172689,
    AUTHOR = {Kamienny, S.},
     TITLE = {Torsion points on elliptic curves and {$q$}-coefficients of
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      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G05 (11F30 11G18 14H52)},
  MRNUMBER = {MR1172689 (93h:11054)},
MRREVIEWER = {Glenn Stevens},
}
@article {MR1956081,
    AUTHOR = {Kaneko, Hiroshi},
     TITLE = {Time-inhomogeneous stochastic processes on the {$p$}-adic
              number field},
   JOURNAL = {Tohoku Math. J. (2)},
  FJOURNAL = {The Tohoku Mathematical Journal. Second Series},
    VOLUME = {55},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {65--87},
      ISSN = {0040-8735},
     CODEN = {TOMJAM},
   MRCLASS = {60H10 (11S85 31C25 60G44)},
  MRNUMBER = {MR1956081 (2004e:60095)},
MRREVIEWER = {Andrzej Madrecki},
}

@book {MR1326374,
    AUTHOR = {Katok, Anatole and Hasselblatt, Boris},
     TITLE = {Introduction to the {M}odern {T}heory of {D}ynamical {S}ystems},
    SERIES = {Encyclopedia of Mathematics and its Applications},
    VOLUME = {54},
      NOTE = {With a supplementary chapter by Katok and Leonardo Mendoza},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {1995},
     PAGES = {xviii+802},
      ISBN = {0-521-34187-6},
   MRCLASS = {58Fxx (34Cxx 34Dxx 58-01 58F11 58F15)},
  MRNUMBER = {MR1326374 (96c:58055)},
MRREVIEWER = {Edoh Amiran},
}

@article {kawaguchi:periodicpts,
    AUTHOR = {Kawaguchi, Shu},
     TITLE = {Some remarks on rational periodic points},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {6},
      YEAR = {1999},
    NUMBER = {5-6},
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      ISSN = {1073-2780},
   MRCLASS = {14G05 (11G35 11G50)},
  MRNUMBER = {2001g:14035},
}

@article{arxiv0405007,
    AUTHOR = {Kawaguchi, Shu},
     TITLE = {Canonical height functions for affine plane automorphisms},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {335},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {285--310},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11G50 (32H50 37F10)},
  MRNUMBER = {MR2221115},
}

@article {arxiv0405006,
    AUTHOR = {Kawaguchi, Shu},
     TITLE = {Canonical heights, invariant currents, and dynamical
              eigensystems of morphisms for line bundles},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {597},
      YEAR = {2006},
     PAGES = {135--173},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {14Gxx (11G50 37Fxx)},
  MRNUMBER = {MR2264317},
}

@article {kawrandom2005,
    AUTHOR = {Kawaguchi, Shu},
     TITLE = {Canonical heights for random iterations in certain varieties},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2007},
    NUMBER = {7},
     PAGES = {Art. ID rnm 023, 33},
      ISSN = {1073-7928},
   MRCLASS = {11G50 (14G25)},
  MRNUMBER = {MR2345343 (2009a:11136)},
MRREVIEWER = {Matthew H. Baker},
}

@article {kawtopent2005,
    AUTHOR = {Kawaguchi, Shu},
     TITLE = {Projective surface automorphisms of positive topological
              entropy from an arithmetic viewpoint},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {130},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {159--186},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {14G25 (11G35 14J50 37B40)},
  MRNUMBER = {MR2382145 (2008m:14042)},
MRREVIEWER = {Yuri Tschinkel},
}

@comment{UPDATE}
@misc {arxiv0909.3573,
    AUTHOR = {Kawaguchi, Shu},
    TITLE = {Local and global canonical height functions for 
         affine space regular automorphisms},
     YEAR = {2009},
     NOTE = {\url{arXiv:0909.3573}},
}

@article {kawsilidht2006,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {Dynamics of projective morphisms having identical canonical
              heights},
   JOURNAL = {Proc. Lond. Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {95},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {519--544},
      ISSN = {0024-6115},
   MRCLASS = {11G50 (14G40 37F50)},
  MRNUMBER = {MR2352570 (2008j:11076)},
MRREVIEWER = {Matthew H. Baker},
      NOTE = {Addendum: Proc. Lond. Math. Soc. (3) 97 (2008), 272},
}


@comment{UPDATE}
@misc {kawsilarithcompl2006,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
    TITLE = {Arithmetic complexity of morphisms},
     YEAR = {2006},
     NOTE = {Preprint},
}

@misc {kawsilholdergreen2006,
    AUTHOR = {Kawaguchi, Shu and Silverman, Joseph H.},
     TITLE = {Nonarchimedean {G}reen functions and dynamics on projective
              space},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {262},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {173--197},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {32Uxx (11G25 32Pxx 37F10 37F50)},
  MRNUMBER = {MR2491605},
}

@inproceedings{keen:juliasets, 
   AUTHOR = {Keen, Linda},
    TITLE = {Julia sets of rational maps},
BOOKTITLE = {Complex Dynamical Systems},
     YEAR = {1994},
    PAGES = {71--90},
PUBLISHER = {American Mathematical Society},
   SERIES = {Proceedings of Symposia in Applied Mathematics},
   VOLUME = {49},
     NOTE = {Cincinnati (1994)}
	}

@article {arxiv0511204,
    AUTHOR = {Khamraev, Murod and Mukhamedov, Farrukh},
     TITLE = {On a class of rational {$p$}-adic dynamical systems},
   JOURNAL = {J. Math. Anal. Appl.},
  FJOURNAL = {Journal of Mathematical Analysis and Applications},
    VOLUME = {315},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {76--89},
      ISSN = {0022-247X},
     CODEN = {JMANAK},
   MRCLASS = {37F10 (11S99 37A25)},
  MRNUMBER = {MR2196531 (2006j:37051)},
MRREVIEWER = {Liang-Chung Hsia},
}
@comment{Detailed analysis of dynamics of ax^2/(bx+c)}

@article {MR1696062,
    AUTHOR = {Khrennikov, Andrei},
     TITLE = {{$p$}-adic dynamical systems: description of concurrent
              struggle in a biological population with limited growth},
   JOURNAL = {Dokl. Akad. Nauk},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Doklady Akademii Nauk},
    VOLUME = {361},
      YEAR = {1998},
    NUMBER = {6},
     PAGES = {752--754},
      ISSN = {0869-5652},
   MRCLASS = {92D25 (11S85 11Z05 37E99 37N25)},
  MRNUMBER = {MR1696062 (2000d:92022)},
MRREVIEWER = {Eugen Belokolos},
}
@book {MR1746953,
    AUTHOR = {Khrennikov, Andrei},
     TITLE = {Non-{A}rchimedean analysis: quantum paradoxes, dynamical
              systems and biological models},
    SERIES = {Mathematics and its Applications},
    VOLUME = {427},
 PUBLISHER = {Kluwer Academic Publishers},
   ADDRESS = {Dordrecht},
      YEAR = {1997},
     PAGES = {xviii+371},
      ISBN = {0-7923-4800-1},
   MRCLASS = {81-02 (00A69 11S85 11Z05 46S10 81P05)},
  MRNUMBER = {MR1746953 (2001h:81004)},
MRREVIEWER = {Bing Hong Wang},
}

@article {MR1989827,
    AUTHOR = {Khrennikov, Andrei and Nilsson, Marcus},
     TITLE = {Behaviour of {H}ensel perturbations of {$p$}-adic monomial
              dynamical systems},
   JOURNAL = {Anal. Math.},
  FJOURNAL = {Analysis Mathematica},
    VOLUME = {29},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {107--133},
      ISSN = {0133-3852},
     CODEN = {ANMADK},
   MRCLASS = {11S85 (12J25 37B99)},
  MRNUMBER = {MR1989827 (2004g:11110)},
MRREVIEWER = {Teturo Kamae},
}
@incollection {MR1977444,
    AUTHOR = {Khrennikov, Andrei and Nilsson, Marcus and Nyqvist, Robert},
     TITLE = {The asymptotic number of periodic points of discrete
              polynomial {$p$}-adic dynamical systems},
 BOOKTITLE = {Ultrametric functional analysis (Nijmegen, 2002)},
    SERIES = {Contemp. Math.},
    VOLUME = {319},
     PAGES = {159--166},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2003},
   MRCLASS = {11S20 (37E15 37E99)},
  MRNUMBER = {MR1977444 (2004b:11158)},
MRREVIEWER = {Liang-Chung Hsia},
}
@article {MR1913640,
    AUTHOR = {Khrennikov, Andrei},
     TITLE = {Small denominators in complex {$p$}-adic dynamics},
   JOURNAL = {Indag. Math. (N.S.)},
  FJOURNAL = {Koninklijke Nederlandse Akademie van Wetenschappen.
              Indagationes Mathematicae. New Series},
    VOLUME = {12},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {177--189},
      ISSN = {0019-3577},
   MRCLASS = {11S85 (37F10)},
  MRNUMBER = {MR1913640 (2003e:11128)},
MRREVIEWER = {Manfred Einsiedler},
}

@article{DDNS559, 
   author = {Khrennikov, Andrei},
    title = {{$p$}-Adic discrete dynamical systems and collective behaviour of
          information states in cognitive models},
  journal = {Discrete Dynamics in Nature and Society},
     year = {2000},
   volume = {5},
   number = {1},
    pages = {59-69}
}

@article {MR1858076,
    AUTHOR = {Khrennikov, Andrei and Nilsson, Marcus},
     TITLE = {On the number of cycles of {$p$}-adic dynamical systems},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {90},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {255--264},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11S85 (37F10)},
  MRNUMBER = {MR1858076 (2002g:11172)},
MRREVIEWER = {Liang-Chung Hsia},
}
@incollection {MR1924983,
    AUTHOR = {Khrennikov, Andrei and Lindahl, Karl-Olof and Gundlach,
              Matthias},
     TITLE = {Ergodicity in the {$p$}-adic framework},
 BOOKTITLE = {Operator {M}ethods in {O}rdinary and {P}artial {D}ifferential
              {E}quations (Stockholm, 2000)},
    SERIES = {Oper. Theory Adv. Appl.},
    VOLUME = {132},
     PAGES = {245--251},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2002},
   MRCLASS = {37E99 (11S85 37A99)},
  MRNUMBER = {MR1924983 (2003g:37083)},
}
@incollection {MR1830516,
    AUTHOR = {Khrennikov, Andrei},
     TITLE = {Ergodic and non-ergodic behaviour for dynamical systems in
              rings of {$p$}-adic integers},
 BOOKTITLE = {Fourth Italian-Latin American Conference on Applied and
              Industrial Mathematics (Havana, 2001)},
     PAGES = {404--409},
 PUBLISHER = {Inst. Cybern. Math. Phys., Havana},
      YEAR = {2001},
   MRCLASS = {37A45 (11S80 37A05)},
  MRNUMBER = {MR1830516 (2002b:37008)},
MRREVIEWER = {Anatoly N. Kochubei},
}

@book {MR2105195,
    AUTHOR = {Khrennikov, Andrei and Nilson, Marcus},
     TITLE = {{$p$}-adic {D}eterministic and {R}andom {D}ynamics},
    SERIES = {Mathematics and {I}ts Applications},
    VOLUME = {574},
 PUBLISHER = {Kluwer Academic Publishers},
   ADDRESS = {Dordrecht},
      YEAR = {2004},
     PAGES = {xviii+270},
      ISBN = {1-4020-2659-5},
   MRCLASS = {37F99 (11S85 28C10 28D15 37H99 37N25 92B20)},
  MRNUMBER = {MR2105195},
}

@article {math.DS/0701899,
    AUTHOR = {Kingsbery, James and Levin, Alex and Preygel, Anatoly and
              Silva, Cesar E.},
     TITLE = {Measurable dynamics of maps on profinite groups},
   JOURNAL = {Indag. Math. (N.S.)},
  FJOURNAL = {Koninklijke Nederlandse Akademie van Wetenschappen.
              Indagationes Mathematicae. New Series},
    VOLUME = {18},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {561--581},
      ISSN = {0019-3577},
   MRCLASS = {37A15 (28D15)},
  MRNUMBER = {MR2424314},
MRREVIEWER = {Radhakrishnan Nair},
}
@article {MR2439398,
    AUTHOR = {Kingsbery, James and Levin, Alex and Preygel, Anatoly and
              Silva, Cesar E.},
     TITLE = {On measure-preserving {$C\sp 1$} transformations of
              compact-open subsets of non-{A}rchimedean local fields},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {361},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {61--85},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {37P20 (11S85 37A05 37A25 37A45 37F10)},
  MRNUMBER = {MR2439398},
}
@article {MR1326795,
    AUTHOR = {Kisaka, Masashi},
     TITLE = {On some exceptional rational maps},
   JOURNAL = {Proc. Japan Acad. Ser. A Math. Sci.},
  FJOURNAL = {Japan Academy. Proceedings. Series A. Mathematical Sciences},
    VOLUME = {71},
      YEAR = {1995},
    NUMBER = {2},
     PAGES = {35--38},
      ISSN = {0386-2194},
     CODEN = {PJAADT},
   MRCLASS = {30D05 (58F23)},
  MRNUMBER = {MR1326795 (96a:30029)},
MRREVIEWER = {I. N. Baker},
}
@comment{gives conjugacy classes of maps for I.N. Baker's description
of rational maps lacking a complex periodic point of some order}
@article {kiwi2006,
    AUTHOR = {Kiwi, Jan},
     TITLE = {Puiseux series polynomial dynamics and iteration of complex cubic
                     polynomials},
   JOURNAL = {Ann. Inst. Fourier (Grenoble)},
  FJOURNAL = {Universit\'e de Grenoble. Annales de l'Institut Fourier},
    VOLUME = {56},
      YEAR = {2006},
    NUMBER = {5},
     PAGES = {1337--1404},
}
@comment{Rivera-Letelier notes: Kiwi shows that there are no wandering
domains for polynomial maps of degree 3 in the field of Puiseaux
series (the main result of this paper shows a deep connection between
ultrametric and complex dynamics)}

@incollection {MR1928528,
    AUTHOR = {Kleinbock, Dmitry and Shah, Nimish and Starkov, Alexander},
     TITLE = {Dynamics of subgroup actions on homogeneous spaces of {L}ie
              groups and applications to number theory},
 BOOKTITLE = {Handbook of {D}ynamical {S}ystems, Vol.\ 1A},
     PAGES = {813--930},
 PUBLISHER = {North-Holland},
   ADDRESS = {Amsterdam},
      YEAR = {2002},
   MRCLASS = {22F30 (11E57 22E30 37A45 37C85)},
  MRNUMBER = {MR1928528 (2004b:22021)},
MRREVIEWER = {Mikhail S. Kulikov},
}

@book {MR1193029,
    AUTHOR = {Knapp, Anthony W.},
     TITLE = {Elliptic {C}urves},
    SERIES = {Mathematical Notes},
    VOLUME = {40},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, NJ},
      YEAR = {1992},
     PAGES = {xvi+427},
      ISBN = {0-691-08559-5},
   MRCLASS = {11G05 (11-01 11F11 14H52)},
  MRNUMBER = {MR1193029 (93j:11032)},
MRREVIEWER = {Joseph H. Silverman},
}

@book {MR1216136,
    AUTHOR = {Koblitz, Neal},
     TITLE = {Introduction to {E}lliptic {C}urves and {M}odular {F}orms},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {97},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
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      YEAR = {1993},
     PAGES = {x+248},
      ISBN = {0-387-97966-2},
   MRCLASS = {11G05 (11F11 11F37 11G40 14H52)},
  MRNUMBER = {MR1216136 (94a:11078)},
}
@book {MR754003,
    AUTHOR = {Koblitz, Neal},
     TITLE = {{$p$}-adic {N}umbers, {$p$}-adic {A}nalysis, and {Z}eta-{F}unctions},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {58},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1984},
     PAGES = {xii+150},
      ISBN = {0-387-96017-1},
   MRCLASS = {11Q25 (11S80)},
  MRNUMBER = {MR754003 (86c:11086)},
}

@incollection {arxiv0608105,
    AUTHOR = {Kra, Bryna},
     TITLE = {Ergodic methods in additive combinatorics},
 BOOKTITLE = {Additive combinatorics},
    SERIES = {CRM Proc. Lecture Notes},
    VOLUME = {43},
     PAGES = {103--143},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2007},
   MRCLASS = {37A30 (11B25 37A45 47A35)},
  MRNUMBER = {MR2359470 (2008k:37018)},
MRREVIEWER = {Tom Sanders},
}
@comment{Survey article based on four lectures}


@comment{--LLL-- }

@incollection {lagarias:numbertheoryanddynamics,
    AUTHOR = {Lagarias, J. C.},
     TITLE = {Number theory and dynamical systems},
 BOOKTITLE = {The {U}nreasonable {E}ffectiveness of {N}umber {T}heory (Orono, ME,
              1991)},
    SERIES = {Proc. Sympos. Appl. Math.},
    VOLUME = {46},
     PAGES = {35--72},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1992},
   MRCLASS = {11Z50 (11K50 58F27 82D25)},
  MRNUMBER = {MR1195841 (93m:11143)},
MRREVIEWER = {M. Mend{\`e}s France},
}
@misc {arxiv0608208,
    AUTHOR = {Lagarias, J. C.},
    TITLE = {The $3x+1$ Problem: {A}n Annotated Bibliography, {I} \& {I}{I}},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.NT/0309224}, \url{ArXiv:math.NT/0608208}},
}

@article {lagariassloan2004,
    AUTHOR = {Lagarias, J. C. and Sloane, N. J. A.},
     TITLE = {Approximate squaring},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {13},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {113--128},
      ISSN = {1058-6458},
   MRCLASS = {11K31 (11B83)},
  MRNUMBER = {MR2065571 (2005c:11098)},
MRREVIEWER = {Thomas Ward},
}

@book{lang:numbertheory,
    AUTHOR = {Lang, Serge},
     TITLE = {Algebraic {N}umber {T}heory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {110},
   EDITION = {Second},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1994},
     PAGES = {xiv+357},
      ISBN = {0-387-94225-4},
   MRCLASS = {11Rxx (11-01 11-02)},
  MRNUMBER = {MR1282723 (95f:11085)},
MRREVIEWER = {M. Ram Murty},
}

@book{lang:diophantinegeometry, 
    AUTHOR = {Lang, Serge},
     TITLE = {Fundamentals of {D}iophantine {G}eometry},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1983},
     PAGES = {xviii+370},
      ISBN = {0-387-90837-4},
   MRCLASS = {11-02 (11Dxx 11Gxx 14G25)},
  MRNUMBER = {MR715605 (85j:11005)},
MRREVIEWER = {Gerd Faltings},
}

@book{lang:algebra, 
    AUTHOR = {Lang, Serge},
     TITLE = {Algebra},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {211},
   EDITION = {third},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2002},
     PAGES = {xvi+914},
      ISBN = {0-387-95385-X},
   MRCLASS = {00A05 (15-02)},
  MRNUMBER = {MR1878556 (2003e:00003)},
}

@book {MR518817,
    AUTHOR = {Lang, Serge},
     TITLE = {Elliptic {C}urves: {D}iophantine {A}nalysis},
    SERIES = {Grund\-leh\-ren der Mathematischen Wissenschaften},
    VOLUME = {231},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1978},
     PAGES = {xi+261},
      ISBN = {3-540-08489-4},
   MRCLASS = {10B15 (10Fxx 14G25)},
  MRNUMBER = {MR518817 (81b:10009)},
MRREVIEWER = {A. J. van der Poorten},
}

@book {langalgabelianfncs,
    AUTHOR = {Lang, Serge},
     TITLE = {Introduction to {A}lgebraic and {A}belian {F}unctions},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1982},
   EDITION = {2},
}
@book {MR890960,
    AUTHOR = {Lang, Serge},
     TITLE = {Elliptic {F}unctions},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {112},
   EDITION = {Second},
      NOTE = {With an appendix by J. Tate},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1987},
     PAGES = {xii+326},
      ISBN = {0-387-96508-4},
   MRCLASS = {11F03 (11G05 11G07 11G15 14G25)},
  MRNUMBER = {MR890960 (88c:11028)},
}

@article{lattes:iteration, 
   AUTHOR = {S. Latt\`es},
    TITLE = {Sur l'iteration des substitutions rationelles et les fonctions de {P}oincar{\'{e}}},
  JOURNAL = {Comptes Rendus Acad. Sci. Paris},
   VOLUME = {166},
     YEAR = {1918},
    PAGES = {26--28}
	}

@techreport{lauschleicher:irreducibility,
   AUTHOR = {Lau, E. and Schleicher, D.},
    TITLE = {Internal addresses in the {M}andelbrot set and 
                   irreducibility of polynomials},
    MONTH = {December},
     YEAR = {1994},
PUBLISHER = {SUNY StonyBrook},
   SERIES = {Institute for Mathematical Sciences Preprint},
   NUMBER = {1994/19}
	}

@article {MR1914256,
    AUTHOR = {Laubie, Fran{\c{c}}ois and Movahhedi, Abbas and Salinier,
              Alain},
     TITLE = {Syst\`emes dynamiques non archim\'ediens et corps des normes},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {132},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {57--98},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11S15 (14L05 37F99)},
  MRNUMBER = {MR1914256 (2003f:11179)},
MRREVIEWER = {Jean-Pierre Wintenberger},
}

@inproceedings{laurent:lehmer, 
   AUTHOR = {Laurent, M.},
    TITLE = {Minoration de la hauteur de {N}\'eron-{T}ate},
BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres},
     YEAR = {1983},
    PAGES = {137--151},
PUBLISHER = {Birkh\"auser},
   SERIES = {Progress in Mathematics},
     NOTE = {Paris 1981--1982}
}

@comment{UPDATE}
@misc {arxiv0909.3107,
    AUTHOR = {Lee, ChongGyu},
    TITLE = {An upper bound for the height for regular affine 
        automorphisms of $\mathbb{A}^n$},
     YEAR = {2009},
     NOTE = {\url{arXiv:0909.3107}},
}

@article {MR1503118,
    AUTHOR = {Lehmer, D. H.},
     TITLE = {Factorization of certain cyclotomic functions},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {34},
      YEAR = {1933},
    NUMBER = {3},
     PAGES = {461--479},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {Database Expansion Item},
  MRNUMBER = {MR1503118},
}

@comment{UPDATE}
@misc {arxiv0809.0379,
    AUTHOR = {Levin, Genadi},
    TITLE = {Multipliers of periodic orbits in spaces of rational maps, I-II},
     YEAR = {2009},
     NOTE = {\url{arXiv:0809.0379}},
}
@COMMENT{Defines operator T_f for a rational map f that
takes a function psi and gives a new function T_f(psi). Paper
proves an interesting identity, which author notes is then formally
true for maps over any characteristic 0 field. Question: How about
characteristic p?}

@article {MR1376996,
    AUTHOR = {Levin, G. and Przytycki, F.},
     TITLE = {When do two rational functions have the same {J}ulia set?},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {125},
      YEAR = {1997},
    NUMBER = {7},
     PAGES = {2179--2190},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {58F23 (30D05)},
  MRNUMBER = {MR1376996 (97i:58149)},
MRREVIEWER = {Walter Bergweiler},
}

@comment{UPDATE}
@misc {arxiv0903.1318,
    AUTHOR = {Levy, Alon},
    TITLE = {The Space of Morphisms on Projective Space},
     YEAR = {2009},
     NOTE = {\url{arXiv:0903.1318}},
}

@article{lewis:invariantset, 
   AUTHOR = {D.J. Lewis},
    TITLE = {Invariant set of morphisms on projective and affine number spaces},
  JOURNAL = {Journal of Algebra},
   VOLUME = {20},
     YEAR = {1972},
    PAGES = {419--434}
	}

@article {li:isogenies,
    AUTHOR = {Li, Hua-Chieh},
     TITLE = {Isogenies between dynamics of formal groups},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {62},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {284--297},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11S31 (11S99 14L05)},
  MRNUMBER = {MR1432775 (98a:11164)},
MRREVIEWER = {Kenneth Kramer},
}


@article {li:commutingpowerseries,
   AUTHOR = {Li, Hua-Chieh},
    TITLE = {$p$-adic power series which commute under composition},
  JOURNAL = {Trans. Amer. Math. Soc.},
 FJOURNAL = {Transactions of the American Mathematical Society},
   VOLUME = {349},
     YEAR = {1997},
   NUMBER = {4},
    PAGES = {1437--1446},
}
@article {li:countingperiodicpoints,
   AUTHOR = {Li, Hua-Chieh},
    TITLE = {Counting periodic points of $p$-adic power series},
  JOURNAL = {Compositio Math.},
 FJOURNAL = {Compositio Mathematica},
   VOLUME = {100},
     YEAR = {1996},
   NUMBER = {3},
    PAGES = {351--364},
}
@article{li:padicperiodicsen, 
   AUTHOR = {Li, Hua-Chieh},
    TITLE = {$p$-adic periodic points and {S}en's theorem},
  JOURNAL = {J. Number Theory},
 FJOURNAL = {Journal of Number Theory},
   VOLUME = {56},
     YEAR = {1996},
   NUMBER = {2},
    PAGES = {309--318},
	}
@article {li:padicdynamics,
   AUTHOR = {Li, Hua-Chieh},
    TITLE = {$p$-adic dynamical systems and formal groups},
  JOURNAL = {Compositio Math.},
 FJOURNAL = {Compositio Mathematica},
   VOLUME = {104},
     YEAR = {1996},
   NUMBER = {1},
    PAGES = {41--54},
}
@article {li:whenendomorphism,
   AUTHOR = {Li, Hua-Chieh},
    TITLE = {When is a $p$-adic power series an endomorphism of a formal
             group?},
  JOURNAL = {Proc. Amer. Math. Soc.},
 FJOURNAL = {Proceedings of the American Mathematical Society},
   VOLUME = {124},
     YEAR = {1996},
   NUMBER = {8},
    PAGES = {2325--2329},
}

@article {MR1896102,
    AUTHOR = {Li, Hua-Chieh},
     TITLE = {On dynamics of power series over unramified extensions of
              {$\mathbb{Q}\sb p$}},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {545},
      YEAR = {2002},
     PAGES = {183--200},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11S31 (37B99 37E99)},
  MRNUMBER = {MR1896102 (2003b:11126)},
MRREVIEWER = {Fran{\c{c}}ois Laubie},
}
@article {MR1883692,
    AUTHOR = {Li, Hua-Chieh},
     TITLE = {{$p$}-typical dynamical systems and formal groups},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {130},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {75--88},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11S31 (11S85)},
  MRNUMBER = {MR1883692 (2003b:11125)},
MRREVIEWER = {Michael E. Zieve},
}
@article {MR1862116,
    AUTHOR = {Li, Hua-Chieh},
     TITLE = {On heights of {$p$}-adic dynamical systems},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {130},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {379--386 (electronic)},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {11S31 (11S99)},
  MRNUMBER = {MR1862116 (2002k:11212)},
MRREVIEWER = {Michael E. Zieve},
}

@book {MR1429394,
    AUTHOR = {Lidl, Rudolf and Niederreiter, Harald},
     TITLE = {Finite {F}ields},
    SERIES = {Encyclopedia of Mathematics and Its Applications},
    VOLUME = {20},
   EDITION = {Second},
      NOTE = {With a foreword by P. M.\ Cohn},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {1997},
     PAGES = {xiv+755},
      ISBN = {0-521-39231-4},
   MRCLASS = {11Txx},
  MRNUMBER = {MR1429394 (97i:11115)},
}

@article{lindward:solenoids, 
    AUTHOR = {Lind, Douglas and Ward, Tom},
     TITLE = {Automorphisms of solenoids and {$p$}-adic entropy},
   JOURNAL = {Ergodic Theory Dynam. Systems},
  FJOURNAL = {Ergodic Theory and Dynamical Systems},
    VOLUME = {8},
      YEAR = {1988},
    NUMBER = {3},
     PAGES = {411--419},
      ISSN = {0143-3857},
   MRCLASS = {28D20 (58F11)},
  MRNUMBER = {MR961739 (90a:28031)},
MRREVIEWER = {Kenneth R. Berg},
}

@incollection {MR1928527,
    AUTHOR = {Lind, Douglas and Schmidt, Klaus},
     TITLE = {Symbolic and algebraic dynamical systems},
 BOOKTITLE = {Handbook of {D}ynamical {S}ystems, Vol.\ 1A},
     PAGES = {765--812},
 PUBLISHER = {North-Holland},
   ADDRESS = {Amsterdam},
      YEAR = {2002},
   MRCLASS = {37B50 (37A15 37B10)},
  MRNUMBER = {MR1928527 (2003h:37017)},
MRREVIEWER = {Anthony Quas},
}
@article {MR1062797,
    AUTHOR = {Lind, Douglas and Schmidt, Klaus and Ward, Tom},
     TITLE = {Mahler measure and entropy for commuting automorphisms of
              compact groups},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {101},
      YEAR = {1990},
    NUMBER = {3},
     PAGES = {593--629},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {22D40 (28D20)},
  MRNUMBER = {MR1062797 (92j:22013)},
MRREVIEWER = {Meir Smorodinsky},
}
@article {MR2057125,
    AUTHOR = {Lindahl, Karl-Olof},
     TITLE = {On {S}iegel's linearization theorem for fields of prime
              characteristic},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {17},
      YEAR = {2004},
    NUMBER = {3},
     PAGES = {745--763},
      ISSN = {0951-7715},
     CODEN = {NONLE5},
   MRCLASS = {37F50 (11S05 37F10)},
  MRNUMBER = {MR2057125 (2005a:37078)},
MRREVIEWER = {Franco Vivaldi},
}

@article {MR1804200,
    AUTHOR = {Lubin, Jonathan},
     TITLE = {Formal flows on the non-{A}rchimedean open unit disk},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {124},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {123--136},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11S99 (30D05 30G35 54H20)},
  MRNUMBER = {MR1804200 (2002a:11139)},
MRREVIEWER = {Liang-Chung Hsia},
}

@article {MR1215030,
    AUTHOR = {Lubin, Jonathan},
     TITLE = {Sen's theorem on iteration of power series},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {123},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {63--66},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {11S31},
  MRNUMBER = {MR1215030 (95c:11138)},
MRREVIEWER = {Robert Gold},
}
@article {MR1310863,
    AUTHOR = {Lubin, Jonathan},
     TITLE = {Non-{A}rchimedean dynamical systems},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {94},
      YEAR = {1994},
    NUMBER = {3},
     PAGES = {321--346},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11S31 (11S99 14L05 58F99)},
  MRNUMBER = {MR1310863 (96g:11140)},
MRREVIEWER = {Ivan Fesenko},
}

@UNPUBLISHED{lubinunpub96,
  AUTHOR = {Lubin, Jonathan},
 TITLE   = {Seminar on $p$-adic time in nonarchimedean dynamical systems},
 NOTE    = {Seminar at {Brown} {University}},
 YEAR    = {prepared April 25, 1996}
}

@article {arxiv0610504,
    AUTHOR = {Lubin, Jonathan D. and Sarkis, Ghassan Y.},
     TITLE = {Extrinsic properties of automorphism groups of formal groups},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {315},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {874--884},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {14L05},
  MRNUMBER = {MR2351898 (2008g:14078)},
MRREVIEWER = {Fran{\c{c}}ois Laubie},
}

@comment{--MMM-- }

@article {Mahler35,
    AUTHOR = {Mahler, Kurt},
     TITLE = {On the lattice points on curves of genus {$1$}},
   JOURNAL = {Proc. Lond. Math. Soc., II. Ser.},
  FJOURNAL = {Proceedings of the London Mathematical Society. Second Series},
    VOLUME = {39},
      YEAR = {1935},
     PAGES = {431--466},
}

@phdthesis{manesthesis, 
    AUTHOR = {Manes, Michelle},
     TITLE = {Arithmetic Dynamics and Moduli Spaces of Rational Maps},
   SCHOOL = {Brown University},
     YEAR = {2007},
}

@article {MR2407816,
    AUTHOR = {Manes, Michelle},
     TITLE = {{$\mathbb{Q}$}-rational cycles for degree-2 rational maps having
              an automorphism},
   JOURNAL = {Proc. Lond. Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {96},
      YEAR = {2008},
    NUMBER = {3},
     PAGES = {669--696},
      ISSN = {0024-6115},
   MRCLASS = {14G25 (11G99)},
  MRNUMBER = {MR2407816 (2009a:14029)},
MRREVIEWER = {Dipendra Prasad},
}

@comment{UPDATE}
@misc {arxiv0902.1813,
    AUTHOR = {Manes, Michelle},
    TITLE = {Moduli spaces for families of rational maps on {$\mathbb{P}^1$}},
     YEAR = {2009},
     NOTE = {\url{arXiv:0902.1813}},
}


@phdthesis{marcellothesis, 
    AUTHOR = {Marcello, Sandra},
     TITLE = {Sur la dynamique arithm\'etique des automorphismes affines},
   SCHOOL = {Universit\'e Paris 7},
     YEAR = {2000},
}

@article {marcello:CR2000,
    AUTHOR = {Marcello, Sandra},
     TITLE = {Sur les propri\'et\'es arithm\'etiques des it\'er\'es
              d'auto\-mor\-phismes r\'eguliers},
   JOURNAL = {C.~R.~Acad. Sci. Paris S\'er. I Math.},
  FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
              Math\'ematique},
    VOLUME = {331},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {11--16},
      ISSN = {0764-4442},
     CODEN = {CASMEI},
   MRCLASS = {11G50},
  MRNUMBER = {2001d:11072},
}

@article {MR1988948,
    AUTHOR = {Marcello, Sandra},
     TITLE = {Sur la dynamique arithm\'etique des automorphismes de l'espace
              affine},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {131},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {229--257},
      ISSN = {0037-9484},
     CODEN = {BSMFAA},
   MRCLASS = {11G50 (32M17 37F10)},
  MRNUMBER = {MR1988948 (2004d:11053)},
MRREVIEWER = {Yuri Tschinkel},
}

@misc {arxiv0310434,
    AUTHOR = {Marcello, Sandra},
    TITLE = {G\'eom\'etrie, points rationnels et it\'er\'es 
                   des automorphismes de l'espace affine},
     YEAR = {2003},
     NOTE = {\url{ArXiv:math.NT/0310434}},
}

@misc {arxiv0310454,
    AUTHOR = {Marcello, Sandra},
    TITLE = {Sur des invariants g\'eom\'etriques associ\'es
                   aux automorphismes du plan affine},
     YEAR = {2003},
     NOTE = {\url{ArXiv:math.AG/0310454}},
}

@misc {arxiv0310417,
    AUTHOR = {Marcello, Sandra},
    TITLE = {Sur la dynamique p-adique arithm\'etique des 
                 automorphismes de l'espace affine},
     YEAR = {2003},
     NOTE = {\url{ArXiv:math.NT/0310417}},
}
@comment{?? the preceding three arxiv articles by Marcello are unlikely
to ever be published}

@article {masser:lehmer,
    AUTHOR = {Masser, D. W.},
     TITLE = {Counting points of small height on elliptic curves},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {117},
      YEAR = {1989},
    NUMBER = {2},
     PAGES = {247--265},
      ISSN = {0037-9484},
     CODEN = {BSMFAA},
   MRCLASS = {11G05 (11D25)},
  MRNUMBER = {MR1015810 (90k:11068)},
MRREVIEWER = {Michel Laurent},
}
@article {arxiv0705.2182,
    AUTHOR = {Masuda, Ariane M. and Zieve, Michael E.},
     TITLE = {Rational functions with linear relations},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {136},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {1403--1408},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {39B12 (12F10 30D05)},
  MRNUMBER = {MR2367113 (2008k:39045)},
MRREVIEWER = {Vassileios Drakopoulos},
}
@article {mazur:uniformbound,
    AUTHOR = {Mazur, B.},
     TITLE = {Modular curves and the {E}isenstein ideal},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications
              Math\'ematiques},
    NUMBER = {47},
      YEAR = {1977},
     PAGES = {33--186 (1978)},
      ISSN = {0073-8301},
     CODEN = {PMIHA6},
   MRCLASS = {14G25 (10D05)},
  MRNUMBER = {MR488287 (80c:14015)},
MRREVIEWER = {M. Ohta},
}

@incollection {mcmillan:integmap,
    AUTHOR = {McMillan, E. M.},
     TITLE = {A problem in the stability of periodic systems},
 BOOKTITLE = {Topics in Modern Physics: A Tribute to E. U. Condon},
     PAGES = {219--244},
 PUBLISHER = {Colorado Assoc. Univ. Press},
   ADDRESS = {Boulder, CO},
      YEAR = {1971},
}
@comment{The first integrable map of the plane was introduced by
E. M. McMillan \ref[in Topics in modern physics: a tribute to
E. U. Condon, 219--244, Colorado Assoc. Univ. Press, Boulder, CO,
1971], and contained 6 arbitrary parameters. This map was generalized
to an 18-parameter map, that is now commonly called the QRT map.}

@article{mcmullen:rootfinding, 
    AUTHOR = {McMullen, Curtis T.},
     TITLE = {Families of rational maps and iterative root-finding
              algorithms},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {125},
      YEAR = {1987},
    NUMBER = {3},
     PAGES = {467--493},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {58F08 (58C15 65H05)},
  MRNUMBER = {MR890160 (88i:58082)},
MRREVIEWER = {Michael Hurley},
}

@article {MR1896103,
    AUTHOR = {McMullen, Curtis T.},
     TITLE = {Dynamics on {$K3$} surfaces: {S}alem numbers and {S}iegel
              disks},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {545},
      YEAR = {2002},
     PAGES = {201--233},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {37F25 (11F06 32H50 32J15 32Q15 37C40)},
  MRNUMBER = {MR1896103 (2003a:37057)},
MRREVIEWER = {Serge Cantat},
}
@article {MR1713286,
    AUTHOR = {McMullen, Curtis T.},
     TITLE = {From dynamics on surfaces to rational points on curves},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {37},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {119--140},
      ISSN = {0273-0979},
     CODEN = {BAMOAD},
   MRCLASS = {11G30 (32G15 37E30 57M60)},
  MRNUMBER = {MR1713286 (2000j:11093)},
MRREVIEWER = {Joseph H. Silverman},
}

@article {MR1620850,
    AUTHOR = {McMullen, Curtis T. and Sullivan, Dennis P.},
     TITLE = {Quasiconformal homeomorphisms and dynamics. {III}. {T}he
              {T}eichm\"uller space of a holomorphic dynamical system},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {135},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {351--395},
      ISSN = {0001-8708},
     CODEN = {ADMTA4},
   MRCLASS = {58F23 (30C62 30D05 30F60)},
  MRNUMBER = {MR1620850 (99e:58145)},
MRREVIEWER = {Athanase Papadopoulos},
}

@comment{UPDATE}
@misc {arxiv0901.2352,
    AUTHOR = {Medvedev, Alice and Scanlon, Thomas},
    TITLE = {Polynomial dynamics},
     YEAR = {2009},
     NOTE = {\url{arXiv:0901.2352}},
}

@article{merel:uniformbound, 
    AUTHOR = {Merel, Lo{\"{\i}}c},
     TITLE = {Bornes pour la torsion des courbes elliptiques sur les corps
              de nombres},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {124},
      YEAR = {1996},
    NUMBER = {1-3},
     PAGES = {437--449},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G05 (11L05)},
  MRNUMBER = {MR1369424 (96i:11057)},
MRREVIEWER = {Henri Darmon},
}

@article {MR785222,
    AUTHOR = {M{\'e}rindol, Jean-Yves},
     TITLE = {Propri\'et\'es \'el\'ementaires des surfaces {$K3$}},
      NOTE = {Geometry of $K3$ surfaces: moduli and periods (Palaiseau,
              1981/1982)},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {126},
      YEAR = {1985},
     PAGES = {45--57},
      ISSN = {0303-1179},
   MRCLASS = {32J15},
  MRNUMBER = {MR785222},
}

@book {MR559531,
    AUTHOR = {Milne, James S.},
     TITLE = {\'{E}tale {C}ohomology},
    SERIES = {Princeton Mathematical Series},
    VOLUME = {33},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, N.J.},
      YEAR = {1980},
     PAGES = {xiii+323},
      ISBN = {0-691-08238-3},
   MRCLASS = {14-02 (14F20 18F99)},
  MRNUMBER = {MR559531 (81j:14002)},
MRREVIEWER = {G. Horrocks},
}

@article{milnor:quadraticmaps, 
    AUTHOR = {Milnor, John},
     TITLE = {Geometry and dynamics of quadratic rational maps},
      NOTE = {With an appendix by the author and Lei Tan},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {2},
      YEAR = {1993},
    NUMBER = {1},
     PAGES = {37--83},
      ISSN = {1058-6458},
   MRCLASS = {58F20 (30D05 32S70 58F23)},
  MRNUMBER = {MR1246482 (96b:58094)},
MRREVIEWER = {J. S. Joel},
}

@book{milnor:dynamicslectures, 
    AUTHOR = {Milnor, John},
     TITLE = {Dynamics in {O}ne {C}omplex {V}ariable},
 PUBLISHER = {Friedr. Vieweg \& Sohn},
   ADDRESS = {Braunschweig},
      YEAR = {1999},
     PAGES = {viii+257},
      ISBN = {3-528-03130-1},
   MRCLASS = {37Fxx (30D05 37-01)},
  MRNUMBER = {MR1721240 (2002i:37057)},
MRREVIEWER = {Dierk Schleicher},
}

@article {MR1806289,
    AUTHOR = {Milnor, John},
     TITLE = {On rational maps with two critical points},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {9},
      YEAR = {2000},
    NUMBER = {4},
     PAGES = {481--522},
      ISSN = {1058-6458},
   MRCLASS = {37F50 (37F20)},
  MRNUMBER = {MR1806289 (2001k:37074)},
MRREVIEWER = {Peter Ha{\"{\i}}ssinsky},
}

@incollection {milnor:lattesmaps,
    AUTHOR = {Milnor, John},
     TITLE = {On {L}att\`es maps},
 BOOKTITLE = {Dynamics on the {R}iemann sphere},
     PAGES = {9--43},
 PUBLISHER = {Eur. Math. Soc., Z\"urich},
      YEAR = {2006},
   MRCLASS = {37F10 (30D05 37-02)},
  MRNUMBER = {MR2348953},
MRREVIEWER = {Feliks Przytycki},
     NOTE = {\url{ArXiv:math.DS/0402147},
             Stony Brook IMS Preprint \#2004/01},
}


@book {MR2158954,
    AUTHOR = {Morris, Dave Witte},
     TITLE = {Ratner's {T}heorems on {U}nipotent {F}lows},
    SERIES = {Chicago Lectures in Mathematics},
 PUBLISHER = {University of Chicago Press},
   ADDRESS = {Chicago, IL},
      YEAR = {2005},
     PAGES = {xii+203},
      ISBN = {0-226-53983-0; 0-226-53984-9},
   MRCLASS = {37A17 (22E40 22F30 37A25 37A30 37A35)},
  MRNUMBER = {MR2158954 (2006h:37006)},
MRREVIEWER = {Bachir Bekka},
}

@article {morton:quadraticmaps,
    AUTHOR = {Morton, Patrick},
     TITLE = {Arithmetic properties of periodic points of quadratic maps},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {62},
      YEAR = {1992},
    NUMBER = {4},
     PAGES = {343--372},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {12E10 (12F10)},
  MRNUMBER = {MR1199627 (93k:12004)},
MRREVIEWER = {R. W. K. Odoni},
}

@article {morton:quadraticmaps2,
    AUTHOR = {Morton, Patrick},
     TITLE = {Arithmetic properties of periodic points of quadratic maps.
              {II}},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {87},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {89--102},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11G30 (11F03 14G05)},
  MRNUMBER = {MR1665198 (2000c:11103)},
MRREVIEWER = {Nobuhiko Ishida},
}

@article {morton:galoisperiodicpoints,
    AUTHOR = {Morton, Patrick},
     TITLE = {Galois groups of periodic points},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {201},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {401--428},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {12F10},
  MRNUMBER = {MR1612390 (99a:12005)},
MRREVIEWER = {Tara L. Smith},
}

@article {morton:finitefielddynamics,
    AUTHOR = {Morton, Patrick},
     TITLE = {Periods of maps on irreducible polynomials over finite fields},
   JOURNAL = {Finite Fields Appl.},
  FJOURNAL = {Finite Fields and their Applications},
    VOLUME = {3},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {11--24},
      ISSN = {1071-5797},
   MRCLASS = {11G99 (11R58)},
  MRNUMBER = {MR1429040 (98d:11075)},
MRREVIEWER = {Joseph H. Silverman},
}

@article {morton:dynamicalmoduli,
    AUTHOR = {Morton, Patrick},
     TITLE = {On certain algebraic curves related to polynomial maps},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {103},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {319--350},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {14H10 (11G99 11R32 58F03)},
  MRNUMBER = {MR1414593 (97m:14030)},
MRREVIEWER = {Joseph H. Silverman},
}

@article {morton:cubicextensions,
    AUTHOR = {Morton, Patrick},
     TITLE = {Characterizing cyclic cubic extensions by automorphism
              polynomials},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {49},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {183--208},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {12F10 (11R16)},
  MRNUMBER = {MR1305089 (95j:12006)},
MRREVIEWER = {Joseph H. Silverman},
}


@article {mortonpatel:galoisperiodicpoints,
    AUTHOR = {Morton, Patrick and Patel, Pratiksha},
     TITLE = {The {G}alois theory of periodic points of polynomial maps},
   JOURNAL = {Proc. London Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {68},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {225--263},
      ISSN = {0024-6115},
     CODEN = {PLMTAL},
   MRCLASS = {11R32 (39B12)},
  MRNUMBER = {MR1253503 (94i:11090)},
MRREVIEWER = {Joseph H. Silverman},
}

@article {mortonsilverman:rationalperiodicpoints,
    AUTHOR = {Morton, Patrick and Silverman, Joseph H.},
     TITLE = {Rational periodic points of rational functions},
   JOURNAL = {Internat. Math. Res. Notices},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {97--110},
      ISSN = {1073-7928},
   MRCLASS = {11G99 (14E05)},
  MRNUMBER = {MR1264933 (95b:11066)},
MRREVIEWER = {Jeffrey Lin Thunder},
}


@article {mortonsilverman:dynamicalunits,
    AUTHOR = {Morton, Patrick and Silverman, Joseph H.},
     TITLE = {Periodic points, multiplicities, and dynamical units},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {461},
      YEAR = {1995},
     PAGES = {81--122},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G99},
  MRNUMBER = {MR1324210 (96b:11090)},
MRREVIEWER = {Jeffrey Lin Thunder},
}


@article {mortonvivaldi:bifurcations,
    AUTHOR = {Morton, Patrick and Vivaldi, Franco},
     TITLE = {Bifurcations and discriminants for polynomial maps},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {8},
      YEAR = {1995},
    NUMBER = {4},
     PAGES = {571--584},
      ISSN = {0951-7715},
     CODEN = {NONLE5},
   MRCLASS = {11C08 (11R21 30D05 58F14 58F23)},
  MRNUMBER = {MR1342504 (96k:11028)},
MRREVIEWER = {Takehiko Morita},
}


@article {moussa:integersinjuliasets, 
    AUTHOR = {Moussa, Pierre and Geronimo, Jeffrey S. and Bessis, Daniel},
     TITLE = {Ensembles de {J}ulia et propri\'et\'es de localisation des
              familles it\'er\'ees d'entiers alg\'ebriques},
   JOURNAL = {C.~R.~Acad. Sci. Paris S\'er. I Math.},
  FJOURNAL = {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences.
              S\'erie I. Math\'ematique},
    VOLUME = {299},
      YEAR = {1984},
    NUMBER = {8},
     PAGES = {281--284},
      ISSN = {0249-6291},
     CODEN = {CASMEI},
   MRCLASS = {58F22 (11R06)},
  MRNUMBER = {MR761246 (86f:58133)},
MRREVIEWER = {M. Rees},
}
@comment{ The authors prove that algebraic integers in the filled
Julia set are preperiodic. They formulate a Lehmer-type conjecture for
Green's functions associated to polynomials.  }

@incollection {MR848378,
    AUTHOR = {Moussa, Pierre},
     TITLE = {Ensembles de {J}ulia et propri\'et\'es de localisation des
              entiers alg\'ebriques},
 BOOKTITLE = {Seminar on {N}umber {T}heory, 1984--1985 (Talence, 1984/1985)},
     PAGES = {Exp.\ No.\ 21, 10},
 PUBLISHER = {Univ. Bordeaux I},
   ADDRESS = {Talence},
      YEAR = {1985},
   MRCLASS = {11R04 (11J68 30D05 58F08)},
  MRNUMBER = {MR848378 (87i:11141)},
MRREVIEWER = {I. N. Baker},
}


@incollection {moussa:juliasets, 
    AUTHOR = {Moussa, Pierre},
     TITLE = {Diophantine properties of {J}ulia sets},
 BOOKTITLE = {Chaotic {D}ynamics and {F}ractals (Atlanta, Ga., 1985)},
    SERIES = {Notes Rep. Math. Sci. Engrg.},
    VOLUME = {2},
     PAGES = {215--227},
 PUBLISHER = {Academic Press},
   ADDRESS = {Orlando, FL},
      YEAR = {1986},
   MRCLASS = {58F11 (30D05)},
  MRNUMBER = {MR858017},
}

@article {MR2067949,
    AUTHOR = {Mukhamedov, Farruh and Rozikov, Utkir},
     TITLE = {On rational {$p$}-adic dynamical systems},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {10},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {21--31},
      ISSN = {1029-3531},
   MRCLASS = {37F10 (11S85 30D05 30G06 54H20)},
  MRNUMBER = {MR2067949 (2005b:37091)},
}
@comment{Detailed analysis of dynamics of (x+a)/(bx+c)}

@article {MR2423943,
    AUTHOR = {Mukhamedov, F.},
     TITLE = {On the chaotic behavior of a cubic {$p$}-adic dynamical
              system},
   JOURNAL = {Mat. Zametki},
  FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Matematicheskie Zametki},
    VOLUME = {83},
      YEAR = {2008},
    NUMBER = {3},
     PAGES = {468--471},
      ISSN = {0025-567X},
   MRCLASS = {37E99 (11S80 11S85 37B25 37F10)},
  MRNUMBER = {MR2423943 (2009c:37038)},
MRREVIEWER = {Anatoly N. Kochubei},
}
@comment{p-adic dynamics of x^3+ax^3}

@comment{UPDATE}
@misc {arxiv:0712.4049,
    AUTHOR = {Mukhamedov, Farrukh and Rozikov, Utkir},
    TITLE = {On one polynomial $p$-adic dynamical system},
     YEAR = {2007},
 LANGUAGE = {Russian},
     NOTE = {\url{ arXiv:0712.4049}},
}

@incollection {arxiv0608573,
    AUTHOR = {Mukhamedov, Farrukh and Mendes, Jos{\'e} F. F.},
     TITLE = {On chaos of a cubic {$p$}-adic dynamical system},
 BOOKTITLE = {Differential equations, chaos and variational problems},
    SERIES = {Progr. Nonlinear Differential Equations Appl.},
    VOLUME = {75},
     PAGES = {305--315},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2008},
   MRCLASS = {37Bxx (12Jxx 37Exx 54H20)},
  MRNUMBER = {MR2409113},
}

@article {arxiv0702697,
    AUTHOR = {Mukhamedov, Farrukh and Mendes, Jos{\'e} F. F.},
     TITLE = {On the chaotic behavior of a generalized logistic {$p$}-adic
              dynamical system},
   JOURNAL = {J. Differential Equations},
  FJOURNAL = {Journal of Differential Equations},
    VOLUME = {243},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {125--145},
      ISSN = {0022-0396},
     CODEN = {JDEQAK},
   MRCLASS = {37B25 (12J12 37D45 54H20)},
  MRNUMBER = {MR2371782 (2009a:37025)},
MRREVIEWER = {Vladimir S. Anashin},
}

@book {MR0282985,
    AUTHOR = {Mumford, David},
     TITLE = {Abelian {V}arieties},
    SERIES = {Tata Institute of Fundamental Research Studies in Mathematics,
              No. 5 },
 PUBLISHER = {Published for the Tata Institute of Fundamental Research,
              Bombay},
      YEAR = {1970},
     PAGES = {viii+242},
   MRCLASS = {14.51},
  MRNUMBER = {MR0282985 (44 \#219)},
MRREVIEWER = {J. S. Milne},
}
@incollection {MR0437531,
    AUTHOR = {Mumford, David and Suominen, Kalevi},
     TITLE = {Introduction to the theory of moduli},
 BOOKTITLE = {Algebraic {G}eometry, Oslo 1970 (Proc. Fifth Nordic
              Summer-School in Math.)},
     PAGES = {171--222},
 PUBLISHER = {Wolters-Noordhoff},
   ADDRESS = {Groningen},
      YEAR = {1972},
   MRCLASS = {14D20},
  MRNUMBER = {MR0437531 (55 \#10455)},
MRREVIEWER = {H. Popp},
}

@book {mumford:geometricinvarianttheory, 
    AUTHOR = {Mumford, David and Fogarty, John and Kirwan, Frances},
     TITLE = {Geometric {I}nvariant {T}heory},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results
              in Mathematics and Related Areas (2)]},
    VOLUME = {34},
   EDITION = {Third},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1994},
     PAGES = {xiv+292},
      ISBN = {3-540-56963-4},
   MRCLASS = {14D25 (58E05 58F05)},
  MRNUMBER = {MR1304906 (95m:14012)},
MRREVIEWER = {Yi Hu},
}
@book {MR1803093,
    AUTHOR = {Murty, M. Ram},
     TITLE = {Problems in {A}nalytic {N}umber {T}heory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {206},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2001},
     PAGES = {xvi+452},
      ISBN = {0-387-95143-1},
   MRCLASS = {11-01 (11M06 11N05)},
  MRNUMBER = {MR1803093 (2001k:11002)},
MRREVIEWER = {D. R. Heath-Brown},
}

@comment{--NNN-- }

@article {narkpreprint03,
    AUTHOR = {Narkiewicz, W. and Marszalek, Roman},
    TITLE = {Finite polynomial orbits in quadratic rings},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {12},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {91--130},
}

@article {narkiewiczcubic,
    AUTHOR = {Narkiewicz, W.},  
     TITLE = {Polynomial cycles in cubic fields of negative discriminant},
   JOURNAL = {Funct. Approx. Comment. Math.},
  FJOURNAL = {Uniwersytet im. Adama Mickiewicza w Poznaniu. Wydzia\l\
              Matematyki i Informatyki. Functiones et Approximatio
              Commentarii Mathematici},
    VOLUME = {35},
      YEAR = {2006},
     PAGES = {261--270},
}
@article {MR2040692,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Polynomial cycles in certain rings of rationals},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {14},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {529--552},
      ISSN = {1246-7405},
   MRCLASS = {11C08 (11R09 13A99)},
  MRNUMBER = {MR2040692 (2005a:11029)},
MRREVIEWER = {Jean-Luc Chabert},
}
@incollection {MR2001e:11025,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Finite polynomial orbits. {A} survey},
 BOOKTITLE = {Algebraic {N}umber {T}heory and Diophantine {A}nalysis (Graz, 1998)},
     PAGES = {331--338},
 PUBLISHER = {de Gruyter},
   ADDRESS = {Berlin},
      YEAR = {2000},
   MRCLASS = {11C08 (12F05)},
  MRNUMBER = {2001e:11025},
MRREVIEWER = {Mireille Car},
}

}
@article {narkiewicz:survey,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Arithmetics of dynamical systems: a survey},
      NOTE = {Number theory (Liptovsk\'y J\'an, 1995)},
   JOURNAL = {Tatra Mt. Math. Publ.},
  FJOURNAL = {Tatra Mountains Mathematical Publications},
    VOLUME = {11},
      YEAR = {1997},
     PAGES = {69--75},
      ISSN = {1210-3195},
   MRCLASS = {11C08 (11R09 11S05)},
  MRNUMBER = {99b:11018},
MRREVIEWER = {Liang-Chung Hsia},
}

@book {MR97e:11037,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Polynomial {M}appings},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1600},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1995},
     PAGES = {viii+130},
      ISBN = {3-540-59435-3},
   MRCLASS = {11C08 (12E05 13B25 13F20)},
  MRNUMBER = {MR1367962 (97e:11037)},
MRREVIEWER = {Jean-Luc Chabert},
}

@article {narkiewicz:polynomialcycles,
    AUTHOR = {Narkiewicz, W.},
     TITLE = {Polynomial cycles in algebraic number fields},
   JOURNAL = {Colloq. Math.},
  FJOURNAL = {Colloquium Mathematicum},
    VOLUME = {58},
      YEAR = {1989},
    NUMBER = {1},
     PAGES = {151--155},
      ISSN = {0010-1354},
     CODEN = {CQMAAQ},
   MRCLASS = {11R09 (11C08)},
  MRNUMBER = {90k:11135},
MRREVIEWER = {T. Mets{\"a}nkyl{\"a}},
}

@article {narkiewiczpezda:finiteorbits,
    AUTHOR = {Narkiewicz, W. and Pezda, T.},
     TITLE = {Finite polynomial orbits in finitely generated domains},
   JOURNAL = {Monatsh. Math.},
  FJOURNAL = {Monatshefte f\"ur Mathematik},
    VOLUME = {124},
      YEAR = {1997},
    NUMBER = {4},
     PAGES = {309--316},
      ISSN = {0026-9255},
     CODEN = {MNMTA2},
   MRCLASS = {11R09 (11C08 11S05)},
  MRNUMBER = {99b:11117},
MRREVIEWER = {Liang-Chung Hsia},
}
@article {MR0179173,
    AUTHOR = {N{\'e}ron, A.},
     TITLE = {Quasi-fonctions et hauteurs sur les vari\'et\'es ab\'eliennes},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {82},
      YEAR = {1965},
     PAGES = {249--331},
      ISSN = {0003-486X},
   MRCLASS = {14.49 (14.51)},
  MRNUMBER = {MR0179173 (31 \#3424)},
MRREVIEWER = {M. Nagata},
}
@unpublished {nevinsrogers:quadmaps,
   AUTHOR = {M. Nevins and T.D. Rogers},
    TITLE = {Quadratic maps as dynamical systems on the $p$-adic numbers},
     YEAR = {March 2000},
     NOTE = {unpublished, \url{www.maths.ex.ac.uk/~mwatkins/zeta/nevins.pdf}},
}
@comment{Nevins indicated that this project was shelved because
Nilsson published a paper with more general versions of the main
theorems.}

@book {MR546290,
    AUTHOR = {Newstead, P. E.},
     TITLE = {Introduction to {M}oduli {P}roblems and {O}rbit {S}paces},
    SERIES = {Tata Institute of Fundamental Research Lectures on Mathematics
              and Physics},
    VOLUME = {51},
 PUBLISHER = {Tata Institute of Fundamental Research},
   ADDRESS = {Bombay},
      YEAR = {1978},
     PAGES = {vi+183},
      ISBN = {0-387-08851-2},
   MRCLASS = {14-02 (14D20)},
  MRNUMBER = {MR546290 (81k:14002)},
MRREVIEWER = {G. Horrocks},
}
@incollection {MR2042407,
    AUTHOR = {Niederreiter, Harald and Shparlinski, Igor E.},
     TITLE = {Dynamical systems generated by rational functions},
 BOOKTITLE = {Applied Algebra, Algebraic Algorithms and Error-Correcting
              Codes (Toulouse, 2003)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {2643},
     PAGES = {6--17},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2003},
   MRCLASS = {94A45 (11T71 37B10 94-02)},
  MRNUMBER = {MR2042407 (2005a:94047)},
}
@comment{Summary: "We consider dynamical systems generated by
iterations of rational functions over finite fields and residue class
rings. We present a survey of recent developments and outline several
open problems."}

@article {MR2026728,
    AUTHOR = {Nilsson, Marcus},
     TITLE = {Fuzzy cycles of {$p$}-adic monomial dynamical systems},
   JOURNAL = {Far East J. Dyn. Syst.},
  FJOURNAL = {Far East Journal of Dynamical Systems},
    VOLUME = {5},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {149--173},
      ISSN = {0972-1118},
   MRCLASS = {37E99 (12J25 39A11)},
  MRNUMBER = {MR2026728 (2004k:37085)},
MRREVIEWER = {Liang-Chung Hsia},
}

@incollection {MR1838295,
    AUTHOR = {Nilsson, Marcus},
     TITLE = {Distribution of cycles of monomial {$p$}-adic dynamical
              systems},
 BOOKTITLE = {$p$-adic {F}unctional {A}nalysis (Ioannina, 2000)},
    SERIES = {Lecture Notes in Pure and Appl. Math.},
    VOLUME = {222},
     PAGES = {233--242},
 PUBLISHER = {Dekker},
   ADDRESS = {New York},
      YEAR = {2001},
   MRCLASS = {37E99 (11S99 37A45 37A99)},
  MRNUMBER = {MR1838295 (2002d:37065)},
MRREVIEWER = {Anatoly N. Kochubei},
}
@article {MR1769981,
    AUTHOR = {Nilsson, Marcus},
     TITLE = {Cycles of monomial and perturbated monomial {$p$}-adic
              dynamical systems},
   JOURNAL = {Ann. Math. Blaise Pascal},
  FJOURNAL = {Annales Math\'ematiques Blaise Pascal},
    VOLUME = {7},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {37--63},
      ISSN = {1259-1734},
   MRCLASS = {11S80 (37B99 37E99)},
  MRNUMBER = {MR1769981 (2001d:11118)},
MRREVIEWER = {Anatoly N. Kochubei},
}
@article {MR2099883,
    AUTHOR = {Nilsson, Marcus and Nyqvist, Robert},
     TITLE = {The asymptotic number of periodic points of discrete
              {$p$}-adic dynamical systems},
   JOURNAL = {Tr. Mat. Inst. Steklova},
  FJOURNAL = {Trudy Matematicheskogo Instituta Imeni V. A. Steklova.
              Rossi\u\i skaya Akademiya Nauk},
    VOLUME = {245},
      YEAR = {2004},
    NUMBER = {Izbr. Vopr. $p$-adich. Mat. Fiz. i Anal.},
     PAGES = {210--217},
      ISSN = {0371-9685},
   MRCLASS = {37F99 (11S85 37C25)},
  MRNUMBER = {MR2099883 (2005h:37103)},
MRREVIEWER = {Liang-Chung Hsia},
}
@incollection {nishizawa91,
    AUTHOR = {Nishizawa, K. and Sekiguchi, K. and Yoshino, K.},
     TITLE = {Location of algebraic integers and related topics},
 BOOKTITLE = {Dynamical Systems and Related Topics (Nagoya, 1990)},
    SERIES = {Adv. Ser. Dyn. Syst.},
    VOLUME = {9},
     PAGES = {422--450},
 PUBLISHER = {World Sci. Publishing},
      YEAR = {1991},
}
@article {MR0037865,
    AUTHOR = {Niven, Ivan},
     TITLE = {The iteration of certain arithmetic functions},
   JOURNAL = {Canadian J. Math.},
    VOLUME = {2},
      YEAR = {1950},
     PAGES = {406--408},
   MRCLASS = {10.0X},
  MRNUMBER = {MR0037865 (12,318m)},
MRREVIEWER = {H. N. Shapiro},
}
@article{northcott:periodicpoints, 
    AUTHOR = {Northcott, D. G.},
     TITLE = {Periodic points on an algebraic variety},
   JOURNAL = {Ann. of Math. (2)},
    VOLUME = {51},
      YEAR = {1950},
     PAGES = {167--177},
   MRCLASS = {14.0X},
  MRNUMBER = {MR0034607 (11,615c)},
MRREVIEWER = {B. Segre},
}

@incollection {MR1838296,
    AUTHOR = {Nyqvist, Robert},
     TITLE = {Some dynamical systems in finite field extensions of the
              {$p$}-adic numbers},
 BOOKTITLE = {$p$-adic functional analysis (Ioannina, 2000)},
    SERIES = {Lecture Notes in Pure and Appl. Math.},
    VOLUME = {222},
     PAGES = {243--253},
 PUBLISHER = {Dekker},
   ADDRESS = {New York},
      YEAR = {2001},
   MRCLASS = {37E99 (11S85 37B99)},
  MRNUMBER = {MR1838296 (2002d:37066)},
MRREVIEWER = {Anatoly N. Kochubei},
}

@comment{--OOO-- }

@article {MR1418355,
    AUTHOR = {Odoni, R. W. K.},
     TITLE = {On the {G}alois groups of iterated generic additive
              polynomials},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {121},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {1--6},
      ISSN = {0305-0041},
     CODEN = {MPCPCO},
   MRCLASS = {12F10},
  MRNUMBER = {MR1418355 (98g:12004)},
}
@article {MR962740,
    AUTHOR = {Odoni, R. W. K.},
     TITLE = {Realising wreath products of cyclic groups as {G}alois groups},
   JOURNAL = {Mathematika},
  FJOURNAL = {Mathematika. A Journal of Pure and Applied Mathematics},
    VOLUME = {35},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {101--113},
      ISSN = {0025-5793},
     CODEN = {MTKAAB},
   MRCLASS = {12F10 (20E22)},
  MRNUMBER = {MR962740 (90a:12013)},
MRREVIEWER = {Antonio Jos{\'e} Engler},
}
@article {MR805714,
    AUTHOR = {Odoni, R. W. K.},
     TITLE = {The {G}alois theory of iterates and composites of polynomials},
   JOURNAL = {Proc. London Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {51},
      YEAR = {1985},
    NUMBER = {3},
     PAGES = {385--414},
      ISSN = {0024-6115},
     CODEN = {PLMTAL},
   MRCLASS = {12E10 (11B37 30F10)},
  MRNUMBER = {MR805714 (87c:12005)},
MRREVIEWER = {K. Kiyek},
}
@article {MR813379,
    AUTHOR = {Odoni, R. W. K.},
     TITLE = {On the prime divisors of the sequence {$w\sb {n+1}=1+w\sb
              1\cdots w\sb n$}},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {32},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {1--11},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11N37 (11B37)},
  MRNUMBER = {MR813379 (87b:11094)},
MRREVIEWER = {W. Narkiewicz},
}
@article {MR0369301,
    AUTHOR = {Oselies, Reinhard and Zieschang, Heiner},
     TITLE = {Ergodische {E}igenschaften der {A}utomorphismen {$p$}-adischer
              {Z}ahlen},
   JOURNAL = {Arch. Math. (Basel)},
    VOLUME = {26},
      YEAR = {1975},
     PAGES = {144--153},
   MRCLASS = {10K10 (28A65)},
  MRNUMBER = {MR0369301 (51 \#5536)},
MRREVIEWER = {Roland Fischer},
}
@comment{UPDATE}
@misc {arxiv0906.3854,
    AUTHOR = {Ostafe, Alina},
    TITLE = {Multivariate Permutation Polynomial Systems 
            and Nonlinear Pseudorandom Number Generators},
     YEAR = {2009},
     NOTE = {\url{arXiv:0906.3854}},
}
@comment{UPDATE}
@misc {arxiv0902.3884,
    AUTHOR = {Ostafe, Alina and Shparlinski, Igor},
    TITLE = {On the degree growth in some polynomial dynamical systems and
          nonlinear pseudorandom number generators},
     YEAR = {2009},
     NOTE = {\url{arXiv:0902.3884}},
}
@comment{UPDATE}
@misc {arxiv0909.3972,
    AUTHOR = {Ostafe, Alina and Shparlinski, Igor},
    TITLE = {On the Length of Critical Orbits of Stable Quadratic Polynomials},
     YEAR = {2009},
     NOTE = {\url{arXiv:0909.3972}},
}

@comment{--PPP-- }

@article {arxiv0901.2646,
    AUTHOR = {Pakapongpun, Apisit and Ward, Thomas},
     TITLE = {Functorial orbit counting},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {12},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {Article 09.2.4, 20},
      ISSN = {1530-7638},
   MRCLASS = {11B83},
  MRNUMBER = {MR2486259},
}

@article {pal07,
    AUTHOR = {P{\'a}l, Ambrus},
     TITLE = {On the torsion of the {M}ordell-{W}eil group of the {J}acobian
              of {D}rinfeld modular curves},
   JOURNAL = {Doc. Math.},
  FJOURNAL = {Documenta Mathematica},
    VOLUME = {10},
      YEAR = {2005},
     PAGES = {131--198 (electronic)},
      ISSN = {1431-0635},
   MRCLASS = {11G18 (11G09)},
  MRNUMBER = {MR2148073 (2006c:11070)},
MRREVIEWER = {Mihran Papikian},
}

@incollection {MR1913468,
    AUTHOR = {Peinado, A. and Montoya, F. and Mu{\~n}oz, J. and Yuste, A.
              J.},
     TITLE = {Maximal periods of {$x\sp 2+c$} in {$\mathbb{F}\sb q$}},
 BOOKTITLE = {Applied Algebra, Algebraic Algorithms and Error-Correcting
              Codes (Melbourne, 2001)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {2227},
     PAGES = {219--228},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2001},
   MRCLASS = {94A55 (11T71 94A60)},
  MRNUMBER = {MR1913468 (2003d:94065)},
}
@comment{Summary: "The orbits produced by the iterations of the mapping
$x\mapsto x^2+c$, defined over $\mathbb{F}_q$, are studied. Several upper
bounds for their periods are obtained, depending on the coefficient
$c$ and the number of elements $q$."}

@article {percival:chaoticmotion,
    AUTHOR = {Percival, Ian and Vivaldi, Franco},
     TITLE = {Arithmetical properties of strongly chaotic motions},
   JOURNAL = {Phys. D},
  FJOURNAL = {Physica D. Nonlinear Phenomena},
    VOLUME = {25},
      YEAR = {1987},
    NUMBER = {1-3},
     PAGES = {105--130},
      ISSN = {0167-2789},
     CODEN = {PDNPDT},
   MRCLASS = {58F13},
  MRNUMBER = {MR887460 (88g:58120)},
MRREVIEWER = {Richard Cushman},
}
@article {arxiv0709.3879,
    AUTHOR = {Petsche, Clayton},
     TITLE = {{$S$}-integral preperiodic points by dynamical systems over
              number fields},
   JOURNAL = {Bull. Lond. Math. Soc.},
  FJOURNAL = {Bulletin of the London Mathematical Society},
    VOLUME = {40},
      YEAR = {2008},
    NUMBER = {5},
     PAGES = {749--758},
      ISSN = {0024-6093},
   MRCLASS = {11G50 (11R04 37Exx)},
  MRNUMBER = {MR2439640},
}

@comment{UPDATE}
@misc {arxiv0806.1364,
    AUTHOR = {Petsche, Clayton and Szpiro, Lucien and Tepper, Michael},
    TITLE = {Isotriviality is equivalent to potential good reduction 
             for endomorphisms of ${\mathbb{P}}^{N}$ over function fields},
     YEAR = {2008},
     NOTE = {\url{arxiv.org/abs/0806.1364}},
}
@article {MR1875166,
    AUTHOR = {Pettigrew, J. and Roberts, John A. G. and Vivaldi, Franco},
     TITLE = {Complexity of regular invertible {$p$}-adic motions},
   JOURNAL = {Chaos},
  FJOURNAL = {Chaos. An Interdisciplinary Journal of Nonlinear Science},
    VOLUME = {11},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {849--857},
      ISSN = {1054-1500},
     CODEN = {CHAOEH},
   MRCLASS = {37F99 (11Z05 37B10 37E15)},
  MRNUMBER = {MR1875166 (2002j:37064)},
}

@article {pezda:rationalcycles,
   AUTHOR = {Pezda, T.},
    TITLE = {Cycles of rational mappings in algebraically closed fields of
             positive characteristics},
     NOTE = {Number theory (Cieszyn, 1998)},
  JOURNAL = {Ann. Math. Sil.},
 FJOURNAL = {Annales Mathematicae Silesianae},
   VOLUME = {12},
     YEAR = {1998},
    PAGES = {15--21},
}
@article {pezda:polynomialcycles3,
   AUTHOR = {Pezda, T.},
    TITLE = {Cycles of polynomials in algebraically closed fields of
             positive characteristic},
  JOURNAL = {Colloq. Math.},
 FJOURNAL = {Colloquium Mathematicum},
   VOLUME = {67},
     YEAR = {1994},
   NUMBER = {2},
    PAGES = {187--195},
}
@article {pezda:polynomialcycles4,
   AUTHOR = {Pezda, T.},
    TITLE = {Cycles of polynomials in algebraically closed fields of
             positive chracteristic. {I}{I}},
  JOURNAL = {Colloq. Math.},
 FJOURNAL = {Colloquium Mathematicum},
   VOLUME = {71},
     YEAR = {1996},
   NUMBER = {1},
    PAGES = {23--30},
}
@article {pezda:polynomialcycles2,
   AUTHOR = {Pezda, T.},
    TITLE = {Cycles of polynomial mappings in several variables},
  JOURNAL = {Manuscripta Math.},
 FJOURNAL = {Manuscripta Mathematica},
   VOLUME = {83},
     YEAR = {1994},
   NUMBER = {3-4},
    PAGES = {279--289},
}
@article {pezda:polynomialcycles,
   AUTHOR = {Pezda, T.},
    TITLE = {Polynomial cycles in certain local domains},
  JOURNAL = {Acta Arith.},
 FJOURNAL = {Acta Arithmetica},
   VOLUME = {66},
     YEAR = {1994},
   NUMBER = {1},
    PAGES = {11--22},
}
@article {MR1974518,
    AUTHOR = {Pezda, T.},
     TITLE = {Cycles of polynomial mappings in several variables over rings
              of integers in finite extensions of the rationals},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {108},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {127--146},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11C08 (13F20)},
  MRNUMBER = {MR1974518 (2004e:11023)},
MRREVIEWER = {Michael E. Zieve},
}
@article {MR1943028,
    AUTHOR = {Pezda, T.},
     TITLE = {On cycles and orbits of polynomial mappings {$\mathbb{Z}\sp
              2\mapsto\mathbb{Z}\sp 2$}},
   JOURNAL = {Acta Math. Inform. Univ. Ostraviensis},
  FJOURNAL = {Acta Mathematica et Informatica Universitatis Ostraviensis},
    VOLUME = {10},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {95--102},
      ISSN = {1211-4774},
     CODEN = {AMIUOA},
   MRCLASS = {11R04 (11S05)},
  MRNUMBER = {MR1943028 (2003m:11174)},
MRREVIEWER = {Michel Grandcolas},
}

@article {arxiv:0802.4016,
    AUTHOR = {Pila, Jonathan and Zannier, Umberto},
     TITLE = {Rational points in periodic analytic sets and the
              {M}anin-{M}umford conjecture},
   JOURNAL = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei
              (9) Mat. Appl.},
  FJOURNAL = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze
              Fisiche, Matematiche e Naturali. Rendiconti Lincei. Serie IX.
              Matematica e Applicazioni},
    VOLUME = {19},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {149--162},
      ISSN = {1120-6330},
   MRCLASS = {11J95 (11G10 14G05)},
  MRNUMBER = {MR2411018 (2009d:11110)},
MRREVIEWER = {Pavlos Tzermias},
}

@comment{UPDATE}
@misc {arxiv0610737,
    AUTHOR = {Pineiro, Jorge},
    TITLE = {Mahler formula on the projective $n$-space},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.NT/0610737}},
}
@comment{26 pages}

@comment{UPDATE}
@misc {arxiv0803.3468,
    AUTHOR = {Pineiro, Jorge},
    TITLE = {Canonical metrics of commuting maps},
     YEAR = {2008},
     NOTE = {\url{arXiv:0803.3468}},
}

@incollection {szpiro04,
    AUTHOR = {Pineiro, Jorge and Szpiro, Lucien and Tucker, Thomas J.},
     TITLE = {Mahler measure for dynamical systems on {${\mathbb{P}}\sp 1$} and
              intersection theory on a singular arithmetic surface},
 BOOKTITLE = {Geometric Methods In Algebra and Number Theory},
    SERIES = {Progr. Math.},
    VOLUME = {235},
     PAGES = {219--250},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {2005},
   MRCLASS = {14G40 (11G50 11R04 37F10)},
  MRNUMBER = {MR2166086 (2006f:14026)},
MRREVIEWER = {Robin de Jong},
}

@article {poonen:uniformboundrefined,
   AUTHOR = {Poonen, Bjorn},
    TITLE = {The classification of rational preperiodic points of quadratic
             polynomials over $\mathbb{Q}$: a refined conjecture},
  JOURNAL = {Math. Z.},
 FJOURNAL = {Mathematische Zeitschrift},
   VOLUME = {228},
     YEAR = {1998},
   NUMBER = {1},
    PAGES = {11--29},
}

@article {MR1873399,
    AUTHOR = {Puri, Yash and Ward, Thomas},
     TITLE = {Arithmetic and growth of periodic orbits},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {4},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {Article 01.2.1, 18 pp. (electronic)},
      ISSN = {1530-7638},
   MRCLASS = {11B83},
  MRNUMBER = {MR1873399 (2002i:11026)},
MRREVIEWER = {Manfred Einsiedler},
}
@article {MR1866354,
    AUTHOR = {Puri, Yash and Ward, Thomas},
     TITLE = {A dynamical property unique to the {L}ucas sequence},
   JOURNAL = {Fibonacci Quart.},
  FJOURNAL = {The Fibonacci Quarterly. The Official Journal of the Fibonacci
              Association},
    VOLUME = {39},
      YEAR = {2001},
    NUMBER = {5},
     PAGES = {398--402},
      ISSN = {0015-0517},
     CODEN = {FIBQAU},
   MRCLASS = {37B10 (11B39)},
  MRNUMBER = {MR1866354 (2002j:37020)},
MRREVIEWER = {Ali Messaoudi},
}

@comment{--QQQ-- }

@article {MR924318,
    AUTHOR = {Quispel, G. R. W. and Roberts, J. A. G. and Thompson, C. J.},
     TITLE = {Integrable mappings and soliton equations},
   JOURNAL = {Phys. Lett. A},
  FJOURNAL = {Physics Letters. A},
    VOLUME = {126},
      YEAR = {1988},
    NUMBER = {7},
     PAGES = {419--421},
      ISSN = {0375-9601},
     CODEN = {PYLAAG},
   MRCLASS = {58F07 (82A99)},
  MRNUMBER = {MR924318 (88m:58084)},
MRREVIEWER = {Peter L. Christiansen},
}
@article {MR982386,
    AUTHOR = {Quispel, G. R. W. and Roberts, J. A. G. and Thompson, C. J.},
     TITLE = {Integrable mappings and soliton equations. {II}},
   JOURNAL = {Phys. D},
  FJOURNAL = {Physica D. Nonlinear Phenomena},
    VOLUME = {34},
      YEAR = {1989},
    NUMBER = {1-2},
     PAGES = {183--192},
      ISSN = {0167-2789},
     CODEN = {PDNPDT},
   MRCLASS = {58F07 (82A68)},
  MRNUMBER = {MR982386 (90e:58066)},
MRREVIEWER = {Peter L. Christiansen},
}
@comment{The first integrable map of the plane was introduced by
E. M. McMillan \ref[in Topics in modern physics: a tribute to
E. U. Condon, 219--244, Colorado Assoc. Univ. Press, Boulder, CO,
1971], and contained 6 arbitrary parameters. This map was generalized
to an 18-parameter map, that is now commonly called the QRT map.}

@comment{--RRR-- }

@article {MR818097,
    AUTHOR = {Rausch, Ulrich},
     TITLE = {On a theorem of {D}obrowolski about the product of conjugate
              numbers},
   JOURNAL = {Colloq. Math.},
  FJOURNAL = {Colloquium Mathematicum},
    VOLUME = {50},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {137--142},
      ISSN = {0010-1354},
     CODEN = {CQMAAQ},
   MRCLASS = {11R06 (11J68)},
  MRNUMBER = {MR818097 (87i:11144)},
MRREVIEWER = {E. Dobrowolski},
}
@article {MR688265,
    AUTHOR = {Raynaud, M.},
     TITLE = {Courbes sur une vari\'et\'e ab\'elienne et points de torsion},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {71},
      YEAR = {1983},
    NUMBER = {1},
     PAGES = {207--233},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14H25 (14G25 14K15)},
  MRNUMBER = {MR688265 (84c:14021)},
MRREVIEWER = {F. Oort},
}
@incollection {MR717600,
    AUTHOR = {Raynaud, M.},
     TITLE = {Sous-vari\'et\'es d'une vari\'et\'e ab\'elienne et points de
              torsion},
 BOOKTITLE = {Arithmetic and Geometry, Vol. I},
    SERIES = {Progr. Math.},
    VOLUME = {35},
     PAGES = {327--352},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1983},
   MRCLASS = {14K05 (32K10)},
  MRNUMBER = {MR717600 (85k:14022)},
MRREVIEWER = {Daniel Coray},
}
@article{rees:deg2moduli, 
    AUTHOR = {Rees, Mary},
     TITLE = {A partial description of parameter space of rational maps of
              degree two. {I}},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {168},
      YEAR = {1992},
    NUMBER = {1-2},
     PAGES = {11--87},
      ISSN = {0001-5962},
     CODEN = {ACMAA8},
   MRCLASS = {58F23 (30D05)},
  MRNUMBER = {MR1149864 (93f:58205)},
MRREVIEWER = {Feliks Przytycki},
}

@article{rees:deg2moduli2, 
    AUTHOR = {Rees, Mary},
     TITLE = {A partial description of the parameter space of rational maps
              of degree two. {II}},
   JOURNAL = {Proc. London Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {70},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {644--690},
      ISSN = {0024-6115},
     CODEN = {PLMTAL},
   MRCLASS = {58F23 (30D05)},
  MRNUMBER = {MR1317518 (96g:58161)},
MRREVIEWER = {Feliks Przytycki},
}

@article {rice07,
    AUTHOR = {Rice, Brian},
     TITLE = {Primitive prime divisors in polynomial arithmetic dynamics},
   JOURNAL = {Integers},
  FJOURNAL = {Integers. Electronic Journal of Combinatorial Number Theory},
    VOLUME = {7},
      YEAR = {2007},
     PAGES = {A26, 16 pp. (electronic)},
      ISSN = {1553-1732},
   MRCLASS = {11B83 (11A41)},
  MRNUMBER = {MR2312276 (2008e:11030)},
MRREVIEWER = {Thomas Ward},
}

@article {MR1501186,
    AUTHOR = {Ritt, J. F.},
     TITLE = {Periodic functions with a multiplication theorem},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {23},
      YEAR = {1922},
    NUMBER = {1},
     PAGES = {16--25},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {30E99},
  MRNUMBER = {MR1501186},
}

@article {MR2018827,
    AUTHOR = {Rivera-Letelier, Juan},
     TITLE = {Espace hyperbolique {$p$}-adique et dynamique des fonctions
              rationnelles},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {138},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {199--231},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {37F10 (11S85 37E25)},
  MRNUMBER = {MR2018827 (2004k:37090)},
MRREVIEWER = {Serge Cantat},
}
@article {MR1937110,
    AUTHOR = {Rivera-Letelier, Juan},
     TITLE = {Une caract\'erisation des fonctions holomorphes injectives en
              analyse ultram\'etrique},
   JOURNAL = {C.~R.~Math. Acad. Sci. Paris},
  FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
    VOLUME = {335},
      YEAR = {2002},
    NUMBER = {5},
     PAGES = {441--446},
      ISSN = {1631-073X},
   MRCLASS = {12J27 (30G35)},
  MRNUMBER = {MR1937110 (2003i:12015)},
MRREVIEWER = {Abdelbaki Boutabaa},
}

@comment{UPDATE} 
@misc {arxiv0412180,
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Sur la structure des ensembles de {F}atou $p$-adiques},
     YEAR = {2002},
     NOTE = {\url{ArXiv:math.DS/0412180}},
}
@comment{35 pages ?? Should this be changed to unpublished?}

@article {arxiv0406417,
   AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Wild recurrent critical points},
  JOURNAL = {J. London Math. Soc. (2)},
 FJOURNAL = {Journal of the London Mathematical Society. Second Series},
   VOLUME = {72},
     YEAR = {2005},
   NUMBER = {2},
    PAGES = {305--326},
     ISSN = {0024-6107},
    CODEN = {JLMSAK},
  MRCLASS = {37F50 (11S85 37F10)},
 MRNUMBER = {MR2156656 (2006f:37066)},
MRREVIEWER = {Serge Cantat},
}
@comment{\url{ArXiv:math.DS/0406417}}

@comment{UPDATE}
@misc {arxiv0605676,
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Notes sur la droite projective de {B}erkovich},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.MG/0605676}},
}
@comment{47 pages ?? Should this be changed to unpublished?}

@article {riverappt1,
   AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Points p\'eriodiques des fonctions rationnelles dans l'espace
             hyperbolique {$p$}-adique},
  JOURNAL = {Comment. Math. Helv.},
 FJOURNAL = {Commentarii Mathematici Helvetici. A Journal of the Swiss
             Mathematical Society},
   VOLUME = {80},
     YEAR = {2005},
   NUMBER = {3},
    PAGES = {593--629},
     ISSN = {0010-2571},
  MRCLASS = {37F10 (11S85 37C25 37E99)},
 MRNUMBER = {MR2165204 (2006d:37081)},
MRREVIEWER = {Serge Cantat},
}


@comment{UPDATE}
@misc {riverappt2,
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Polynomials over {$\mathbb{C}_p$} with wandering domains, 
        after {R}. {B}enedetto},
     YEAR = {2006},
     NOTE = {Preprint, \url{www.math.sunysb.edu/~rivera/mypapers/wand.ps}},
}

@comment{UPDATE}
@misc {riverappt3,
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Th\'eorie de {F}atou et {J}ulia dans la droite projective de
            {B}erkovich},
     YEAR = {2007},
     NOTE = {In preparation},
}

@phdthesis{riverathesis, 
    AUTHOR = {Rivera-Letelier, Juan},
    TITLE = {Dynamique des fonctions rationnelles sur des corps locaux},
   SCHOOL = {Universite de {Paris} {X}{I}},
     YEAR = {2000}
}

@article {MR2040006,
    AUTHOR = {Rivera-Letelier, Juan},
     TITLE = {Dynamique des fonctions rationnelles sur des corps locaux},
      NOTE = {Geometric methods in dynamics. II},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {287},
      YEAR = {2003},
     PAGES = {xv, 147--230},
      ISSN = {0303-1179},
   MRCLASS = {37F50 (14G20 30D05 37F10 39B12)},
  MRNUMBER = {MR2040006 (2005f:37100)},
MRREVIEWER = {Serge Cantat},
}
@comment{This is essentially the author's thesis}

@book {MR0352107,
    AUTHOR = {Robert, Alain},
     TITLE = {Elliptic curves},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1973},
     PAGES = {viii+264},
   MRCLASS = {14K15},
  MRNUMBER = {MR0352107 (50 \#4594)},
MRREVIEWER = {Kuang-yen Shih},
}

@article {MR2017601,
    AUTHOR = {Roberts, John A. G. and  Vivaldi, Franco},
     TITLE = {Arithmetical method to detect integrability in maps},
   JOURNAL = {Phys. Rev. Lett.},
  FJOURNAL = {Physical Review Letters},
    VOLUME = {90},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {034102, 4},
      ISSN = {0031-9007},
     CODEN = {PRLTAO},
   MRCLASS = {37J10 (11N36 37C05 37J35)},
  MRNUMBER = {MR2017601 (2004i:37109)},
}
@article {MR2164737,
    AUTHOR = {Roberts, John A. G. and Vivaldi, Franco},
     TITLE = {Signature of time-reversal symmetry in polynomial
              automorphisms over finite fields},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {18},
      YEAR = {2005},
    NUMBER = {5},
     PAGES = {2171--2192},
      ISSN = {0951-7715},
     CODEN = {NONLE5},
   MRCLASS = {37E30 (11T99 37C25 37C80)},
  MRNUMBER = {MR2164737 (2006f:37060)},
MRREVIEWER = {Teturo Kamae},
}
@article {MR1368298,
    AUTHOR = {Rogers, Thomas D.},
     TITLE = {The graph of the square mapping on the prime fields},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {148},
      YEAR = {1996},
    NUMBER = {1-3},
     PAGES = {317--324},
      ISSN = {0012-365X},
     CODEN = {DSMHA4},
   MRCLASS = {11T99 (05C20)},
  MRNUMBER = {MR1368298 (96m:11115)},
MRREVIEWER = {S. D. Cohen},
}
@article {MR2106974,
    AUTHOR = {Ru, Min and Yi, Eunjeong},
     TITLE = {Nevanlinna theory and iteration of rational maps},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {249},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {125--138},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {11J97 (30D05 30D35 37F10)},
  MRNUMBER = {MR2106974 (2005i:11096)},
MRREVIEWER = {William A. Cherry},
}

@book {MR924157,
    AUTHOR = {Rudin, Walter},
     TITLE = {Real and {C}omplex {A}nalysis},
   EDITION = {Third},
 PUBLISHER = {McGraw-Hill Book Co.},
   ADDRESS = {New York},
      YEAR = {1987},
     PAGES = {xiv+416},
      ISBN = {0-07-054234-1},
   MRCLASS = {00A05 (26-01 30-01 46-01)},
  MRNUMBER = {MR924157 (88k:00002)},
}

@article{russowalde:quadraticmaps, 
   Author = {Russo, P. and Walde, R.},
    TITLE = {Rational periodic points of the quadratic function ${Q}_c(x)=x^2+c$},
  JOURNAL = {Am. Math. Monthly},
   VOLUME = {101},
     YEAR = {1994},
    PAGES = {318--331}
	}

@comment{--SSS-- }

@phdthesis{sarkis:thesis, 
   AUTHOR = {Sarkis, Ghassan},
    TITLE = {Formal {G}roups and $p$-adic {D}ynamical {S}ystems},
   SCHOOL = {Brown University},
     YEAR = {2001}
	}
@article {MR2173969,
    AUTHOR = {Sarkis, Ghassan},
     TITLE = {On lifting commutative dynamical systems},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {293},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {130--154},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {11S31 (37C99)},
  MRNUMBER = {MR2173969},
MRREVIEWER = {Fran{\c{c}}ois Laubie},
}
@comment{UPDATE}
@misc {arxiv:0807.4162,
    AUTHOR = {Scanlon, Thomas},
    TITLE = {Analytic relations on a dynamical orbit},
     YEAR = {2008},
     NOTE = {\url{arXiv:0807.4162}},
}
@article {MR1328699,
    AUTHOR = {Schmidt, Wolfgang and Steinmetz, Norbert},
     TITLE = {The polynomials associated with a {J}ulia set},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {27},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {239--241},
      ISSN = {0024-6093},
     CODEN = {LMSBBT},
   MRCLASS = {30D05},
  MRNUMBER = {MR1328699 (96e:30061)},
MRREVIEWER = {Lo Yang},
}
@comment{For any Julia set (of a polynomial) $J$ which is neither a
circle nor a straight line segment, there exists a polynomial $P$ such
that any polynomial with Julia set $J$ can be written in the form
$\sigma P^n$, where $\sigma$ is a rotation mapping $J$ onto itself,
and $n$ is a positive integer.}

@book {MR568710,
    AUTHOR = {Schmidt, Wolfgang},
     TITLE = {Diophantine {A}pproximation},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {785},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1980},
     PAGES = {x+299},
      ISBN = {3-540-09762-7},
   MRCLASS = {10Fxx (10-02)},
  MRNUMBER = {MR568710 (81j:10038)},
MRREVIEWER = {A. J. van der Poorten},
}

@article{schanuel:heights, 
   AUTHOR = {S. Schanuel},
    TITLE = {Heights in number fields},
  JOURNAL = {Bull. Soc. Math. France},
   VOLUME = {107},
     YEAR = {1979},
    PAGES = {443--449},
	}

@PHDTHESIS{schleicherphd94,
 AUTHOR  = {D. Schleicher},
 TITLE   = {Internal addresses in the {M}andelbrot set and irreducibility of polynomials},
 SCHOOL  = {Cornell University},
 ADDRESS = {Ithaca NY},
 YEAR    = {1994},
}

@book{schmidt:algebraicdynamics, 
    AUTHOR = {Schmidt, Klaus},
     TITLE = {Dynamical {S}ystems of {A}lgebraic {O}rigin},
    SERIES = {Progress in Mathematics},
    VOLUME = {128},
 PUBLISHER = {Birkh\"auser Verlag},
   ADDRESS = {Basel},
      YEAR = {1995},
     PAGES = {xviii+310},
      ISBN = {3-7643-5174-8},
   MRCLASS = {28D15 (11K55 22D40 28D20)},
  MRNUMBER = {MR1345152 (97c:28041)},
MRREVIEWER = {Mahesh Nerurkar},
}
@article {MR2135559,
    AUTHOR = {Schweizer, Andreas},
     TITLE = {On periodic points under the iteration of additive
              polynomials},
   JOURNAL = {Manuscripta Math.},
  FJOURNAL = {Manuscripta Mathematica},
    VOLUME = {113},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {25--34},
      ISSN = {0025-2611},
     CODEN = {MSMHB2},
   MRCLASS = {11C08 (11G09 37E15)},
  MRNUMBER = {MR2135559 (2005m:11039)},
MRREVIEWER = {Julie Tzu-Yueh Wang},
}
@book {MR554237,
    AUTHOR = {Serre, Jean-Pierre},
     TITLE = {Local {F}ields},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {67},
      NOTE = {Translated from the French by Marvin Jay Greenberg},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1979},
     PAGES = {viii+241},
      ISBN = {0-387-90424-7},
   MRCLASS = {12Bxx},
  MRNUMBER = {MR554237 (82e:12016)},
}
@book {MR1757192,
    AUTHOR = {Serre, Jean-Pierre},
     TITLE = {Lectures on the {M}ordell-{W}eil {T}heorem},
    SERIES = {Aspects of Mathematics},
   EDITION = {Third},
      NOTE = {Translated from the French and edited by Martin Brown from
              notes by Michel Waldschmidt,
              with a foreword by Brown and Serre},
 PUBLISHER = {Friedr. Vieweg \& Sohn},
   ADDRESS = {Braunschweig},
      YEAR = {1997},
     PAGES = {x+218},
      ISBN = {3-528-28968-6},
   MRCLASS = {11G10 (11D41 11G30 14G25)},
  MRNUMBER = {MR1757192 (2000m:11049)},
}

@comment{UPDATE}
@misc {arxiv0910.5550,
    AUTHOR = {Sha, Min and Hu, Su},
    TITLE = {Monomial Dynamical Systems of Dimension One over Finite Fields},
     YEAR = {2009},
     NOTE = {\url{arXiv:0910.5550}},
}
@article {shimura:fldofdef,
   AUTHOR = {Shimura, Goro},
    TITLE = {On the field of definition for a field of automorphic
             functions. {I}, {I}{I}, {I}{I}{I}},
  JOURNAL = {Ann. of Math. (2)},
   VOLUME = {80, 81, 83},
     YEAR = {1964, 1965, 1966},
    PAGES = {160--189, 124--165, 377--385},
}
@book {MR1291394,
    AUTHOR = {Shimura, Goro},
     TITLE = {Introduction to the {A}rithmetic {T}heory of {A}utomorphic
              {F}unctions},
    SERIES = {Publications of the Mathematical Society of Japan},
    VOLUME = {11},
      NOTE = {Reprint of the 1971 original,
              Kan\^o Memorial Lectures, 1},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, NJ},
      YEAR = {1994},
     PAGES = {xiv+271},
      ISBN = {0-691-08092-5},
   MRCLASS = {11Fxx (11-02 11G05 11G40)},
  MRNUMBER = {MR1291394 (95e:11048)},
}
@article {MR917803,
    AUTHOR = {Shparlinski{\u\i}, I. E.},
     TITLE = {The number of different prime divisors of recurrent sequences},
   JOURNAL = {Mat. Zametki},
  FJOURNAL = {Akademiya Nauk SSSR. Matematicheskie Zametki},
    VOLUME = {42},
      YEAR = {1987},
    NUMBER = {4},
     PAGES = {494--507, 622},
      ISSN = {0025-567X},
   MRCLASS = {11N99 (11B37)},
  MRNUMBER = {MR917803 (89k:11092)},
MRREVIEWER = {Grigori Kolesnik},
}
@article {arxiv0607779,
    AUTHOR = {Shparlinski, Igor},
    TITLE = {On Some Dynamical Systems in Finite Fields and Residue Rings},
   JOURNAL = {Discrete Contin. Dyn. Syst.},
  FJOURNAL = {Discrete and Continuous Dynamical Systems. Series A},
    VOLUME = {17},
      YEAR = {2007},
     PAGES = {901--917},
}

@incollection {sibony:panoramas,
    AUTHOR = {Sibony, Nessim},
     TITLE = {Dynamique des applications rationnelles de {$\mathbb{P}\sp k$}},
 BOOKTITLE = {Dynamique et g\'eom\'etrie complexes (Lyon, 1997)},
    SERIES = {Panor. Synth\`eses},
    VOLUME = {8},
     PAGES = {ix--x, xi--xii, 97--185},
 PUBLISHER = {Soc. Math. France},
   ADDRESS = {Paris},
      YEAR = {1999},
   MRCLASS = {32H50 (37F10 37F50)},
  MRNUMBER = {MR1760844 (2001e:32026)},
MRREVIEWER = {Mattias Jonsson},
}

@incollection {MR2052279,
    AUTHOR = {Sidorov, Nikita},
     TITLE = {Arithmetic dynamics},
 BOOKTITLE = {Topics in Dynamics and Ergodic Theory},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {310},
     PAGES = {145--189},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {2003},
   MRCLASS = {37B10 (11K16 37A45)},
  MRNUMBER = {MR2052279},
MRREVIEWER = {Manfred Einsiedler},
}
@comment{From MR: In this survey paper the author describes a collection of
results dealing with arithmetic expansions of various dynamical
systems---a (to be developed) branch of symbolic dynamics the author
calls arithmetic dynamics.}

@article{siegel:hyperellipticintegerpoints, 
   AUTHOR = {Siegel, C.L.},
    TITLE = {The integer solutions of the equation $y^2=ax^n+bx^{n-1}+\cdots+k$},
  JOURNAL = {J. London Math. Soc.},
   VOLUME = {1},
     YEAR = {1926},
    PAGES = {66--68}
}

@incollection {siegeldiophappr,
   AUTHOR = {Siegel, C.L.},
     TITLE = {{\"U}ber einige {A}nwendungen diophantischer {A}pproximationen},
 BOOKTITLE = {Collected Works},
     PAGES = {209--266},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1966},
}

@book{silverman:aec, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The {A}rithmetic of {E}lliptic {C}urves},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {106},
      NOTE = {Corrected reprint of the 1986 original},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1992},
     PAGES = {xii+400},
      ISBN = {0-387-96203-4},
   MRCLASS = {11G05 (14H52)},
  MRNUMBER = {MR1329092 (95m:11054)},
}

@book{silverman:ataec, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Advanced {T}opics in the {A}rithmetic of {E}lliptic {C}urves},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {151},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1994},
     PAGES = {xiv+525},
      ISBN = {0-387-94328-5},
   MRCLASS = {11G05 (11G07 11G15 11G40 14H52)},
  MRNUMBER = {MR1312368 (96b:11074)},
MRREVIEWER = {Henri Darmon},
}
@book {MR2316407,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The {A}rithmetic of {D}ynamical {S}ystems},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {241},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2007},
     PAGES = {x+511},
      ISBN = {978-0-387-69903-5},
   MRCLASS = {11-01 (11G99 37Bxx 37Fxx)},
  MRNUMBER = {MR2316407},
}
@article {silverman:K3htseries,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {A zeta function over a recurrent sequence},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {106},
      YEAR = {1999},
    NUMBER = {7},
     PAGES = {686--688},
      NOTE = {Problem 10486 with solutions},
}

@article {silverman:integerpointsongenus1,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Integer points on curves of genus {$1$}},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {The Journal of the London Mathematical Society. Second Series},
    VOLUME = {28},
      YEAR = {1983},
    NUMBER = {1},
     PAGES = {1--7},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {10B10 (10J06 14G25 14K15)},
  MRNUMBER = {MR703458 (84g:10033)},
MRREVIEWER = {Michael Laska},
}
@article {MR895285,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {A quantitative version of {S}iegel's theorem: integral points
              on elliptic curves and {C}atalan curves},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {378},
      YEAR = {1987},
     PAGES = {60--100},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G05 (14G25)},
  MRNUMBER = {MR895285 (89g:11047)},
MRREVIEWER = {Toshihiro Hadano},
}
@book {MR1171452,
    AUTHOR = {Silverman, Joseph H. and Tate, John},
     TITLE = {Rational {P}oints on {E}lliptic {C}urves},
    SERIES = {Undergraduate Texts in Mathematics},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1992},
     PAGES = {x+281},
      ISBN = {0-387-97825-9},
   MRCLASS = {11-01 (11D25 11G05 14H52)},
  MRNUMBER = {MR1171452 (93g:11003)},
MRREVIEWER = {Andrew Bremner},
}

@article{silverman:computecanonicalht,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Computing heights on elliptic curves},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {51},
      YEAR = {1988},
    NUMBER = {183},
     PAGES = {339--358},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {11G05 (11D25 11Y40 14G25 14K15)},
  MRNUMBER = {MR942161 (89d:11049)},
MRREVIEWER = {Philippe Satg{\'e}},
}

@article{silverman:K3heights, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Rational points on {$K3$} surfaces: a new canonical height},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {105},
      YEAR = {1991},
    NUMBER = {2},
     PAGES = {347--373},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14G05 (11G35 14J20 14J28)},
  MRNUMBER = {MR1115546 (92k:14025)},
MRREVIEWER = {I. Dolgachev},
}

@article{silverman:dynamicalintegerpoints, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Integer points, {D}iophantine approximation, and iteration of
              rational maps},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {71},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {793--829},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {11G99 (11J99)},
  MRNUMBER = {MR1240603 (95e:11070)},
MRREVIEWER = {Jeffrey Lin Thunder},
}

@article{silverman:henonmap, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Geometric and arithmetic properties of the {H}\'enon map},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {215},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {237--250},
      ISSN = {0025-5874},
     CODEN = {MAZEAX},
   MRCLASS = {14G25 (11G99 14E05 58F20)},
  MRNUMBER = {MR1259460 (95f:14040)},
MRREVIEWER = {Takeshi Ooe},
}

@article{silverman:fieldofdef, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The field of definition for dynamical systems on {$\mathbb{P}\sp
              1$}},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {98},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {269--304},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11G99 (11R27 14E22)},
  MRNUMBER = {MR1351830 (96j:11090)},
MRREVIEWER = {Laurent Denis},
}

@article{silverman:polynomialiterate, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Rational functions with a polynomial iterate},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {180},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {102--110},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {11G99},
  MRNUMBER = {MR1375568 (96j:11091)},
MRREVIEWER = {Jeffrey Lin Thunder},
}

@article{silverman:modulirationalmaps, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {The space of rational maps on {$\mathbb{P}\sp 1$}},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {94},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {41--77},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {14D10 (14L30 26A18 37E99 37F10)},
  MRNUMBER = {MR1635900 (2000m:14010)},
}

@article{silverman:arithdistfunctions, 
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Arithmetic distance functions and height functions in
              {D}iophantine geometry},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {279},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {193--216},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11G99 (11D99 14G99)},
  MRNUMBER = {MR919501 (89a:11066)},
MRREVIEWER = {Andrew Bremner},
}

@article {silverman:htregauts,
    AUTHOR = {Silverman, Joseph H.},
    TITLE = {Height Bounds and Preperiodic Points  for 
         Families of Jointly Regular Affine Maps},
   JOURNAL = {Quart. J. Pure Appl. Math.},
    VOLUME = {2},
      YEAR = {2006},
     PAGES = {135--145},
}

@article {MR2226354,
    AUTHOR = {Silverman, Joseph H. and Stephens, Nelson},
     TITLE = {The sign of an elliptic divisibility sequence},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {21},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {1--17},
      ISSN = {0970-1249},
   MRCLASS = {11G05 (11B83)},
  MRNUMBER = {MR2226354 (2007a:11075)},
MRREVIEWER = {Manfred Einsiedler},
}

@misc {arXiv:0707.1505,
    AUTHOR = {Silverman, Joseph H.},
     TITLE = {Variation of periods modulo {$p$} in arithmetic dynamics},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {14},
      YEAR = {2008},
     PAGES = {601--616},
      ISSN = {1076-9803},
   MRCLASS = {11G35 (11G50 11R45 14G40 37F10)},
  MRNUMBER = {MR2448661},
MRREVIEWER = {Thomas Ward},
}

@comment{UPDATE}
@misc {arxiv0806.2580,
    AUTHOR = {Silverman, Joseph H. and Voloch, Jos\'e Felipe},
    TITLE = {A Local-Global Criterion for Dynamics on {$\mathbb{P}^1$}},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {137},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {285--294},
}
@article{smyth:lehmer, 
    AUTHOR = {Smyth, C. J.},
     TITLE = {On the product of the conjugates outside the unit circle of an
              algebraic integer},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {3},
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     PAGES = {169--175},
      ISSN = {0024-6093},
   MRCLASS = {10.65},
  MRNUMBER = {MR0289451 (44 \#6641)},
MRREVIEWER = {H. W. Brinkmann},
}

@incollection  {arxiv0701397,
    AUTHOR = {Smyth, Chris},
     TITLE = {The {M}ahler measure of algebraic numbers: a survey},
 BOOKTITLE = {Number theory and polynomials},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {352},
     PAGES = {322--349},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {2008},
   MRCLASS = {11R06},
  MRNUMBER = {MR2428530},
}

@comment{UPDATE}
@misc {arxiv:0808.2679,
    AUTHOR = {Sookdeo, Vijay},
    TITLE = {Integer Points in Backward Orbits},
     YEAR = {2008},
     NOTE = {\url{arXiv:0808.2679}},
}


@book {MR1746847,
    AUTHOR = {Starkov, Alexander N.},
     TITLE = {Dynamical systems on homogeneous spaces},
    SERIES = {Translations of Mathematical Monographs},
    VOLUME = {190},
      NOTE = {Translated from the 1999 Russian original by the author},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2000},
     PAGES = {xvi+243},
      ISBN = {0-8218-1389-7},
   MRCLASS = {37A25 (11E04 11H55 22E40 37C85)},
  MRNUMBER = {MR1746847 (2001m:37013b)},
MRREVIEWER = {S. G. Dani},
}

@article {arxiv0704.3674,
    AUTHOR = {Akiyama, Shigeki and Brunotte, Horst and Peth{\H{o}}, Attila
              and Steiner, Wolfgang},
     TITLE = {Periodicity of certain piecewise affine planar maps},
   JOURNAL = {Tsukuba J. Math.},
  FJOURNAL = {Tsukuba Journal of Mathematics},
    VOLUME = {32},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {197--251},
      ISSN = {0387-4982},
   MRCLASS = {37C25 (37E15)},
  MRNUMBER = {MR2433023},
MRREVIEWER = {Peter Ashwin},
}

@article {MR507748,
    AUTHOR = {Stewart, Cameron L.},
     TITLE = {Algebraic integers whose conjugates lie near the unit circle},
   JOURNAL = {Bull. Soc. Math. France},
  FJOURNAL = {Bulletin de la Soci\'et\'e Math\'ematique de France},
    VOLUME = {106},
      YEAR = {1978},
    NUMBER = {2},
     PAGES = {169--176},
      ISSN = {0037-9484},
     CODEN = {BSMFAA},
   MRCLASS = {12A10 (10F40)},
  MRNUMBER = {MR507748 (80a:12002)},
MRREVIEWER = {Christopher Smyth},
}
	
@article {MR1174401,
    AUTHOR = {Stoll, Michael},
     TITLE = {Galois groups over {$\mathbb{Q}$} of some iterated polynomials},
   JOURNAL = {Arch. Math. (Basel)},
  FJOURNAL = {Archiv der Mathematik},
    VOLUME = {59},
      YEAR = {1992},
    NUMBER = {3},
     PAGES = {239--244},
      ISSN = {0003-889X},
     CODEN = {ACVMAL},
   MRCLASS = {12F10 (12E10 12F12)},
  MRNUMBER = {MR1174401 (93h:12004)},
MRREVIEWER = {R. W. K. Odoni},
}
@article {arxiv:0803.2836,
    AUTHOR = {Stoll, Michael},
     TITLE = {Rational 6-cycles under iteration of quadratic polynomials},
   JOURNAL = {LMS J. Comput. Math.},
  FJOURNAL = {LMS Journal of Computation and Mathematics},
    VOLUME = {11},
      YEAR = {2008},
     PAGES = {367--380},
      ISSN = {1461-1570},
   MRCLASS = {11G30 (11D41 11G40 14Gxx)},
  MRNUMBER = {MR2465796},
}

@article {sullivan:nowanderingdomains,
    AUTHOR = {Sullivan, Dennis},
     TITLE = {Quasiconformal homeomorphisms and dynamics. {I}. {S}olution of
              the {F}atou-{J}ulia problem on wandering domains},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {122},
      YEAR = {1985},
    NUMBER = {3},
     PAGES = {401--418},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {58F11 (20H05 30C60 30D05 57R99 58F08)},
  MRNUMBER = {MR819553 (87i:58103)},
MRREVIEWER = {L. Keen},
}

@article {MR2099889,
    AUTHOR = {Svensson, P.-A.},
     TITLE = {Perturbed dynamical systems in {$p$}-adic fields},
   JOURNAL = {Tr. Mat. Inst. Steklova},
  FJOURNAL = {Trudy Matematicheskogo Instituta Imeni V. A. Steklova.
              Rossi\u\i skaya Akademiya Nauk},
    VOLUME = {245},
      YEAR = {2004},
    NUMBER = {Izbr. Vopr. $p$-adich. Mat. Fiz. i Anal.},
     PAGES = {264--272},
      ISSN = {0371-9685},
   MRCLASS = {11S85 (37F10)},
  MRNUMBER = {MR2099889 (2005h:11271)},
MRREVIEWER = {Liang-Chung Hsia},
}

@article {MR1505274,
    AUTHOR = {Sylvester, J. J.},
     TITLE = {On a Point in the Theory of Vulgar Fractions},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {3},
      YEAR = {1880},
    NUMBER = {4},
     PAGES = {332--335},
      ISSN = {0002-9327},
     CODEN = {AJMAAN},
   MRCLASS = {Contributed Item},
  MRNUMBER = {MR1505274},
}
@comment{UPDATE}
@misc {arxiv0510404,
    AUTHOR = {Szpiro, L. and Tucker, T.},
    TITLE = {Equidistribution and generalized {M}ahler measures},
     YEAR = {2006},
     NOTE = {\url{ArXiv:math.NT/0510404}},
}
@comment{30 pages}

@incollection {arxiv0603438,
    AUTHOR = {Szpiro, Lucien and Tucker, Thomas J.},
     TITLE = {On half log discriminant},
 BOOKTITLE = {Diophantine geometry},
    SERIES = {CRM Series},
    VOLUME = {4},
     PAGES = {323--334},
 PUBLISHER = {Ed. Norm., Pisa},
      YEAR = {2007},
   MRCLASS = {11G35},
  MRNUMBER = {MR2349664 (2008k:11071)},
MRREVIEWER = {Charles Favre},
}

@article  {arxiv0603436,
    AUTHOR = {Szpiro, Lucien and Tucker, Thomas J.},
     TITLE = {A {S}hafarevich-{F}altings theorem for rational functions},
   JOURNAL = {Pure Appl. Math. Q.},
  FJOURNAL = {Pure and Applied Mathematics Quarterly},
    VOLUME = {4},
      YEAR = {2008},
    NUMBER = {3, part 2},
     PAGES = {715--728},
      ISSN = {1558-8599},
   MRCLASS = {14G25},
  MRNUMBER = {MR2435841 (2009g:14027)},
MRREVIEWER = {Marco A. Garuti},
}

@article {MR1427622,
    AUTHOR = {Szpiro, L. and Ullmo, E. and Zhang, S.},
     TITLE = {\'{E}quir\'epartition des petits points},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {127},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {337--347},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14G40 (11G35 14G05)},
  MRNUMBER = {MR1427622 (98i:14027)},
MRREVIEWER = {Antoine Chambert-Loir},
}

@comment{--TTT-- }

@article {thiran:padicdynamics,
   AUTHOR = {Thiran, E. and Verstegen, D. and Weyers, J.},
    TITLE = {$p$-adic dynamics},
  JOURNAL = {J. Statist. Phys.},
 FJOURNAL = {Journal of Statistical Physics},
   VOLUME = {54},
     YEAR = {1989},
   NUMBER = {3-4},
    PAGES = {893--913},
}

@phdthesis{thuillier:thesis, 
   AUTHOR = {Thuillier, Amaury},
    TITLE = {Th{\'e}orie du potentiel sur les courbes en
        g{\'e}om{\'e}trie analytique non
        archim{\'e}dienne. {A}pplications \`a la th{\'e}orie
        d'{A}rakelov},
   SCHOOL = {Universit\'e Rennes},
     YEAR = {2005}
}

@comment{--UUU-- }

@article {MR1609514,
    AUTHOR = {Ullmo, Emmanuel},
     TITLE = {Positivit\'e et discr\'etion des points alg\'ebriques des
              courbes},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {147},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {167--179},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {14G40 (11G30 14H25 14H40)},
  MRNUMBER = {MR1609514 (99e:14031)},
MRREVIEWER = {Yuichiro Takeda},
}

@comment{--VVV-- }

@book{vanderwaerden:algebra, 
   AUTHOR = {B.L. van der Waerden},
    TITLE = {Algebra},
  EDITION = {7th},
PUBLISHER = {Frederick Ungar Publ. Co.},
  ADDRESS = {New York},
     YEAR = {1970}
	}

@article {MR2033734,
    AUTHOR = {Vasiga, Troy and Shallit, Jeffrey},
     TITLE = {On the iteration of certain quadratic maps over {${\rm
              GF}(p)$}},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {277},
      YEAR = {2004},
    NUMBER = {1-3},
     PAGES = {219--240},
      ISSN = {0012-365X},
     CODEN = {DSMHA4},
   MRCLASS = {05C20 (11T99)},
  MRNUMBER = {MR2033734 (2004k:05104)},
MRREVIEWER = {Kevin Lawrence McAvaney},
}
@comment{From MR: For a finite set $S$ and a function $f\colon
S\rightarrow S$, the directed graph $G_f$ has vertex set $S$ and
directed edges $(x,f(x))$ for all $x$ in $S$. Thus, $G_f$ depicts the
iterations of $f$: each $x$ induces a path (tail) attached to a
cycle. Motivated by various factoring and prime testing algorithms in
number theory the authors investigate the structure of $G_f$ for
$f(x)=x^2\pmod{p}$ and $f(x)=x^2-2\pmod{p}$ for prime $p$. In
particular they give the complete structure for both functions when
$p$ is a Fermat prime or a Mersenne prime. For general $p$ average
tail and cycle lengths in $G_f$ are determined and some asymptotic
results are given.
For a generalization to f(x)=x^e in finite fields, see:
MR2072394 (2005e:11118) Chou, Wun-Seng(RC-AST); Shparlinski, Igor
E.(5-MCQR-CP) On the cycle structure of repeated exponentiation modulo
a prime. (English summary) J. Number Theory 107 (2004), no. 2,
345--356. }

@incollection {verstegen:padicdynamics,
    AUTHOR = {Verstegen, D.},
     TITLE = {{$p$}-adic dynamical systems},
 BOOKTITLE = {Number {T}heory and {P}hysics (Les Houches, 1989)},
    SERIES = {Springer Proc. Phys.},
    VOLUME = {47},
     PAGES = {235--242},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1990},
   MRCLASS = {58F36 (58F08)},
  MRNUMBER = {MR1058468 (91m:58140)},
MRREVIEWER = {Eugen Belokolos},
}

@article {MR1160332,
    AUTHOR = {Veselov, A. P.},
     TITLE = {Integrable mappings},
   JOURNAL = {Uspekhi Mat. Nauk},
  FJOURNAL = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo.
              Uspekhi Matematicheskikh Nauk},
    VOLUME = {46},
      YEAR = {1991},
    NUMBER = {5(281)},
     PAGES = {3--45, 190},
      ISSN = {0042-1316},
   MRCLASS = {58F07 (14K99 39A12 70H05)},
  MRNUMBER = {MR1160332 (93e:58096)},
MRREVIEWER = {J. S. Joel},
}

@article {vivaldi:irreduciblepolys,
    AUTHOR = {Vivaldi, Franco},
     TITLE = {Dynamics over irreducible polynomials},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {5},
      YEAR = {1992},
    NUMBER = {4},
     PAGES = {941--960},
      ISSN = {0951-7715},
     CODEN = {NONLE5},
   MRCLASS = {11Z50 (11S99 58F08)},
  MRNUMBER = {MR1174225 (93i:11152)},
}

@article {vivaldi:linearmaps,
    AUTHOR = {Vivaldi, Franco},
     TITLE = {Geometry of linear maps over finite fields},
   JOURNAL = {Nonlinearity},
  FJOURNAL = {Nonlinearity},
    VOLUME = {5},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {133--147},
      ISSN = {0951-7715},
     CODEN = {NONLE5},
   MRCLASS = {11T99 (58F22)},
  MRNUMBER = {MR1148792 (93c:11111)},
MRREVIEWER = {Rudolf Lidl},
}

@incollection {vivaldi:hamiltonianchaos,
    AUTHOR = {Vivaldi, Franco},
     TITLE = {Algebraic number theory and {H}amiltonian chaos},
 BOOKTITLE = {Number Theory and Physics (Les Houches, 1989)},
    SERIES = {Springer Proc. Phys.},
    VOLUME = {47},
     PAGES = {294--301},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1990},
   MRCLASS = {58F13 (11R11 58F11)},
  MRNUMBER = {MR1058474 (91i:58093)},
MRREVIEWER = {F. Schweiger},
}
@incollection {vivaldi:arithmeticchaos,
    AUTHOR = {Vivaldi, Franco},
     TITLE = {The arithmetic of chaos},
 BOOKTITLE = {Chaos, Noise and Fractals (Como, 1986)},
    SERIES = {Malvern Phys. Ser.},
    VOLUME = {3},
     PAGES = {187--199},
 PUBLISHER = {Hilger},
   ADDRESS = {Bristol},
      YEAR = {1987},
   MRCLASS = {58F11 (11R11 11R29)},
  MRNUMBER = {MR918575 (89b:58123)},
MRREVIEWER = {F. Schweiger},
}
@article {vivaldi:arithmeticanosov,
    AUTHOR = {Vivaldi, Franco},
     TITLE = {Arithmetical theory of {A}nosov diffeomorphisms},
   JOURNAL = {Proc. Roy. Soc. London Ser. A},
  FJOURNAL = {Proceedings of the Royal Society. London. Series A.
              Mathematical, Physical and Engineering Sciences},
    VOLUME = {413},
      YEAR = {1987},
    NUMBER = {1844},
     PAGES = {97--107},
      ISSN = {0962-8444},
     CODEN = {PRLAAZ},
   MRCLASS = {58F15 (11R99)},
  MRNUMBER = {MR909271 (89a:58090)},
MRREVIEWER = {S. Yu. Pilyugin},
}
@article {MR1367580,
    AUTHOR = {Voutier, Paul},
     TITLE = {An effective lower bound for the height of algebraic numbers},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {74},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {81--95},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11J25 (11R06)},
  MRNUMBER = {MR1367580 (96j:11098)},
MRREVIEWER = {D. Boyd},
}

@comment{--WWW-- }

@incollection {MR1861987,
    AUTHOR = {Waldschmidt, Michel},
     TITLE = {Algebraic dynamics and transcendental numbers},
 BOOKTITLE = {Noise, oscillators and algebraic randomness (Chapelle des
              Bois, 1999)},
    SERIES = {Lecture Notes in Phys.},
    VOLUME = {550},
     PAGES = {372--378},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2000},
   MRCLASS = {37F10 (11J81 37F99)},
  MRNUMBER = {MR1861987 (2002h:37074)},
}

@incollection {MR1352278,
    AUTHOR = {Wang, Lan},
     TITLE = {Rational points and canonical heights on {$K3$}-surfaces in
              {$\mathbb{P}\sp 1\times\mathbb{P}\sp 1\times\mathbb{P}\sp 1$}},
 BOOKTITLE = {Recent Developments in the Inverse Galois Problem (Seattle,
              WA, 1993)},
    SERIES = {Contemp. Math.},
    VOLUME = {186},
     PAGES = {273--289},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1995},
   MRCLASS = {14G05 (11G35 14J28)},
  MRNUMBER = {MR1352278 (97a:14023)},
MRREVIEWER = {Gregory S. Call},
}

@article {ward:sintegerdynamics,
   AUTHOR = {Ward, T. B.},
    TITLE = {Almost all ${S}$-integer dynamical systems have many periodic
             points},
  JOURNAL = {Ergodic Theory Dynam. Systems},
 FJOURNAL = {Ergodic Theory and Dynamical Systems},
   VOLUME = {18},
     YEAR = {1998},
   NUMBER = {2},
}

@book {MR1421575,
    AUTHOR = {Washington, Lawrence C.},
     TITLE = {Introduction to cyclotomic fields},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {83},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1997},
     PAGES = {xiv+487},
      ISBN = {0-387-94762-0},
   MRCLASS = {11R18 (11-01 11-02 11R23)},
  MRNUMBER = {MR1421575 (97h:11130)},
MRREVIEWER = {T. Mets{\"a}nkyl{\"a}},
}

@article {MR925498,
    AUTHOR = {Wehler, Joachim},
     TITLE = {{$K3$}-surfaces with {P}icard number {$2$}},
   JOURNAL = {Arch. Math. (Basel)},
  FJOURNAL = {Archiv der Mathematik. Archives of Mathematics. Archives
              Math\'ematiques},
    VOLUME = {50},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {73--82},
      ISSN = {0003-889X},
     CODEN = {ACVMAL},
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  MRNUMBER = {MR925498 (89b:14054)},
MRREVIEWER = {Shigeyuki Kondo},
}

@book {MR1612686,
    AUTHOR = {Wirsching, G{\"u}nther J.},
     TITLE = {The dynamical system generated by the {$3n+1$} function},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1681},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1998},
     PAGES = {viii+158},
      ISBN = {3-540-63970-5},
   MRCLASS = {11B83 (11B37 11K41 39B12 58F08 60C05 60J10)},
  MRNUMBER = {MR1612686 (99g:11027)},
MRREVIEWER = {J. C. Lagarias},
}

@article {woodcocksmart:chaosprng,
   AUTHOR = {Woodcock, Christopher F. and Smart, Nigel P.},
    TITLE = {$p$-adic chaos and random number generation},
  JOURNAL = {Experiment. Math.},
 FJOURNAL = {Experimental Mathematics},
   VOLUME = {7},
     YEAR = {1998},
   NUMBER = {4},
    PAGES = {333--342},
}

@comment{--XXX-- }

@comment{--YYY-- }

@article {arxiv0612424,
    AUTHOR = {Yuan, Xinyi},
     TITLE = {Big line bundles over arithmetic varieties},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {173},
      YEAR = {2008},
    NUMBER = {3},
     PAGES = {603--649},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14G40 (11G50 11H06 14C20)},
  MRNUMBER = {MR2425137},
}
@comment{Abstract: We prove a Hilbert-Samuel type result of arithmetic
big line bundles in Arakelov geometry, which is an analogue of a
classical theorem of Siu. An application of this result gives
equidistribution of small points over algebraic dynamical systems,
following the work of Szpiro-Ullmo-Zhang. We also generalize
Chambert-Loir's non-archimedean equidistribution.}

@comment{--ZZZ-- }

@article {MR669663,
    AUTHOR = {Zagier, Don},
     TITLE = {On the number of {M}arkoff numbers below a given bound},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {39},
      YEAR = {1982},
    NUMBER = {160},
     PAGES = {709--723},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {10F20 (10A20 10B10)},
  MRNUMBER = {MR669663 (83k:10062)},
MRREVIEWER = {Richard T. Bumby},
}

@incollection {zhang:distalgdyn,
    AUTHOR = {Zhang, Shou-Wu},
     TITLE = {Distributions in algebraic dynamics},
 BOOKTITLE = {Differential Geometry: A Tribute to Professor {S}.-{S}. {C}hern,
                   Surv. Differ. Geom., Vol. X},
     PAGES = {381--430},
 PUBLISHER = {Int. Press},
   ADDRESS = {Boston, MA},
      YEAR = {2006},
}
@comment{This is an overview of a lot of different topics in
arithmetic dynamics, including canonical metrics, equidistribution of
periodic and small points, dynamical Lehmer and Manin-Mumford
conjectures, etc. There is also a video of a talk by Zhang at MSRI
with this title available at 
www.msri.org/communications/vmath/VMathVideos/VideoInfo/2488/show_video}

@article {MR1609518,
    AUTHOR = {Zhang, Shou-Wu},
     TITLE = {Equidistribution of small points on abelian varieties},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {147},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {159--165},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {14G40 (11G10 14G05 14K15)},
  MRNUMBER = {MR1609518 (99e:14032)},
MRREVIEWER = {Yuichiro Takeda},
}

@phdthesis{zieve:thesis, 
   AUTHOR = {M. Zieve},
    TITLE = {Cycles of Polynomial Mappings},
  SCHOOL  = {University of California at Berkeley},
     YEAR = {1996},
     NOTE = {\url{www.math.rutgers.edu/~zieve/papers/ucthesis.ps}},
}

@article {zimmerman:commpolys,
    AUTHOR = {Zimmerman, Karl},
    TITLE = {Commuting polynomials and self-similarity},
   JOURNAL = {New York J. Math.},
  FJOURNAL = {New York Journal of Mathematics},
    VOLUME = {13},
      YEAR = {2007},
     PAGES = {89--96 (electronic)},
}