\newcommand{\au}[1]#1, \newcommand{\ti}[1]#1, \newcommand{\jo}[1]#1 \newcommand{\vo}[1]#1 \newcommand{\yr}[1](#1), \newcommand{\page}[1]#1. \newcommand{\ppx}[1]#1, \newcommand{\pps}[1]#1. \newcommand{\bk}[1]#1, \newcommand{\inbk}[1]in: #1 \newcommand{\xxx}[1]arXiv:#1.

• M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, Dover Publications Inc., New York, 1992, Reprint of the 1972 edition.
• B. Adamczewski and J. P. Bell, On vanishing coefficients of algebraic power series over fields of positive characteristic. Invent. Math. 187 (2012), 343–393.
• A. Akbary and D. Ghioca, Periods of orbits modulo primes, J. Number Theory 129 (2009), 2831–2842.
• J.-P. Allouche and J. Shallit, Automatic sequences. Theory, applications, generalizations. Cambridge University Press, Cambridge, 2003.
• A. Altman and S. Kleiman, Introduction to Grothendieck duality theory, Lecture Notes in Mathematics, Vol. 146, Springer-Verlag, Berlin, 1970.
• E. Amerik, Existence of non-preperiodic algebraic points for a rational self-map of infinite order, Math. Res. Lett. 18 (2011), 251–256.
• E. Amerik, F. Bogomolov, and M. Rovinsky, Remarks on endomorphisms and rational points, Compositio Math. 147 (2011), 1819–1842.
• E. Amerik and F. Campana, Fibrations méromorphes sur certaines variétés à fibré canonique trivial, Pure Appl. Math. Q. 4 (2008), 509–545.
• M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
• P. Autissier, Points entiers sur les surfaces arithmétiques, J. reine. angew. Math 531 (2001), 201–235.
• E. Bach, Toward a theory of Pollard’s rho method, Inform. and Comput. 90 (1991), 139–155.
• \au{M. Baker} \ti{A finiteness theorem for canonical heights attached to rational maps over function fields} \jo{J. Reine Angew. Math.} \vo{626} \yr{2009} \pps{205–233}
• \au{M. Baker and L. DeMarco} \ti{Preperiodic points and unlikely intersections} \jo{Duke Math. J.} \vo{159} \yr{2011} \pps{1–29}
• —, \ti{Special curves and post-critically-finite polynomials} \jo{Forum Math. $\pi$} \vo{1} \yr{2013} \pps{e3, 35 pp}
• \au{M. Baker and L.-C. Hsia} \ti{Canonical heights, transfinite diameters, and polynomial dynamics} \jo{J. reine angew. Math.} \vo{585} \yr{2005} \pps{61–92}
• M. Baker, S.-I. Ih, and R. Rumely, A finiteness property of torsion points, Algebra Number Theory 2 (2008), no. 2, 217–248.
• M. Baker and R. Rumely, Equidistribution of small points, rational dynamics, and potential theory, Ann. Inst. Fourier (Grenoble) 56 (2006), 625–688.
• —, \ti{Potential theory and dynamics on the Berkovich projective line} Mathematics Surveys and Monographs 159, American Mathematical Society, Providence, RI, 2010.
• A. S. Bang, Taltheoretiske Undersogelse, Tidsskrift Mat. 4 (1886), 70–80, 130–137.
• \au{A. Beardon} \ti{Iteration of rational functions} Complex analytic dynamical systems. Graduate Texts in Mathematics 132. Springer-Verlag, New York, 1991.
• J. P. Bell, A generalized Skolem-Mahler-Lech theorem for affine varieties, J. London Math. Soc. (2) 73 (2006), 367–379.
• J. P. Bell, S. N. Burris, K. Yeats, On the set of zero coefficients of a function satisfying a linear differential equation, Math. Proc. Cambridge Philos. Soc. 153 (2012), 235–247.
• J. P. Bell, D. Ghioca, and T. J. Tucker, The dynamical Mordell-Lang problem for étale maps, Amer. J. Math. 132 (2010), 1655–1675.
• —, Applications of $p$-adic analysis for bounding periods of subvarieties under étale maps, Int. Math. Res. Not. IMRN, vol. 2015, 3576–3597.
• —, The Dynamical Mordell-Lang problem for Noetherian spaces, Funct. Approx. Comm. Math. 53 (2015), no. 2, 313–328.
• J. P. Bell, D. Ghioca, and Z. Reichstein, On a dynamical variant of a theorem of Rosenlicht, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) to appear.
• J. P. Bell and J. Lagarias, A Skolem-Mahler-Lech theorem for iterated automorphisms of $K$-algebras, Canad. J. Math. 67 (2015), no. 2, 286–314.
• \au{R. L. Benedetto} \ti{Heights and preperiodic points for polynomials over function fields} \jo{Int. Math. Res. Not.} \vo{62} \yr{2005} \pps{3855–3866}
• \au{R. L. Benedetto, D. Ghioca, P. Kurlberg, and T. J. Tucker} \ti{A gap principle for dynamics} \jo{Compositio Math.} \yr{2010} \vo{146} \pps{1056–1072}
• —, A case of the dynamical Mordell-Lang conjecture (with an Appendix by U. Zannier), Math. Ann. 352 (2012), 1–26.
• \au{R. L. Benedetto, D. Ghioca, B. A. Hutz, P. Kurlberg, T. Scanlon, and T. J. Tucker} \ti{Periods of rational maps modulo primes} \jo{Math. Ann.} \vo{355} \yr{2013} \pps{637–660}
• M. Bennett, Y. Bugeaud, and M. Mignotte, Perfect powers with few binary digits and related Diophantine problems, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 12 (2013), no. 4, 941–953.
• \au{V. Berkovich} \ti{Spectral theory and analytic geometry over non-Archimedean fields} Mathematical Surveys and Monographs 33, American Mathematical Society, Providence, RI, 1990.
• \au{F. Beukers and H. P. Schlickewei} \ti{The equation $x+y=1$ in finitely generated groups} \jo{Acta Arith.} \vo{78} \yr{1996} \pps{189–199}
• \au{J.-P. Bézivin} \ti{Une généralisation du théorème de Skolem-Mahler-Lech} \jo{Quart. J. Math. Oxford Ser. (2)} \vo{40} \yr{1989} \pps{133–138}
• \au{Y. F. Bilu and R. F. Tichy} \ti{The Diophantine equation $f(x)=g(y)$} \jo{Acta Arith.} \vo{95} \yr{2000} \pps{261–288}
• E. Bombieri and W. Gubler, Heights in Diophantine geometry, New Mathematical Monographs, vol. 4, Cambridge University Press, Cambridge, 2006.
• \au{E. Bombieri, D. Masser, and U. Zannier} \ti{Intersecting a curve with algebraic subgroups of multiplicative groups} \jo{IMRN} \vo{20} \yr{1999} \pps{1119–1140}
• A. I. Borevich and I. R. Shafarevich, Number theory, Translated from the Russian by Newcomb Greenleaf. Pure and Applied Mathematics, Vol. 20, Academic Press, New York, 1966.
• V. Bosser, Minorations de formes linéaires de logarithmes pour les modules de Drinfeld, J. Number Theory 75 (1999), no. 2, 279–323.
• N. Bourbaki, Lie groups and Lie algebras. Chapters 1–3, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1998, Translated from the French, Reprint of the 1989 English translation.
• —, Éléments de mathématique. Algèbre commutative. Chapitres 8 et 9, Springer, Berlin, 2006, Reprint of the 1983 original.
• \au{B. Branner and J. H. Hubbard} \ti{The iteration of cubic polynomials. I. The global topology of parameter space.} \jo{Acta Math.} \vo{160(3-4)} \yr{1988} \pps{143-206}
• X. Buff, A. L. Epstein, and S. Koch, Böttcher coordinates, Indiana Univ. Math. J. 61 (2012), no. 5, 1765–1799.
• \au{G. S. Call and J. H. Silverman} \ti{Canonical heights on varieties with morphisms} \jo{Compositio Math.} \vo{89} \yr{1993} \pps{163–205}
• \au{L. Carleson and T. W. Gamelin} \ti{Complex dynamics} Springer-Verlag, New York, 1993.
• C. Chabauty, Sur les points rationnels des courbes algébriques de genre supérieur à l’unité, C. R. Acad. Sci. Paris 212 (1941), 882–885.
• A. Chambert-Loir, Mesures et équidistribution sur les espaces de Berkovich, J. Reine Angew. Math. 595 (2006), 215–235.
• Z. Chatzidakis and E. Hrushovski, Difference fields and descent in algebraic dynamics. I, J. Inst. Math. Jussieu 7 (2008), 635–686.
• —, Difference fields and descent in algebraic dynamics. II, J. Inst. Math. Jussieu 7 (2008), 687–704.
• R. F. Coleman, Effective Chabauty, Duke Math. J. 52 (1985), no. 3, 765–770.
• P. Corvaja and U. Zannier, On the Diophantine equation $f(a^m, y) = b^n$, Acta Arith. 94 (2000), 25–40.
• P. Corvaja and U. Zannier, Finiteness of odd perfect powers with four nonzero binary digits, Ann. Inst. Fourier (Grenoble) 63 (2013), no. 2, 715–731.
• P. Corvaja, V. Sookdeo, T. J. Tucker, and U. Zannier, Integral points in two-parameter orbits, J. Reine Angew. Math., to appear.
• S. D. Cutkosky and V. Srinivas, On a problem of Zariski on dimensions of linear systems, Ann. of Math. (2) 137 (1993), no. 3, 531–559.
• H. Davenport and K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 160–167.
• P. Deligne, La Conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273–307.
• L. Demangos, Some examples toward a Manin-Mumford conjecture for abelian uniformizable $T$-modules, preprint.
• L. DeMarco, X. Wang, and H. Ye, Torsion points and the Lattes family, to appear in Amer. J. Math.
• L. van den Dries and A. Günaydin, The fields of real and complex numbers with a small multiplicative group, Proc. London Math. Soc. 93 (2006), 43–81.
• L. van den Dries, A. Macintyre, and D. Marker, the elementary theory of restricted analytic fields with exponentiation, Ann. Math. 140 (1994), 183–205.
• L. van den Dries and C. Miller, On the real exponential field with restricted analytic functions Israel J. Math. 85 (1994), 19–56.
• L. van den Dries and K. Schmidt, Bounds in the theory of polynomial rings over fields. A nonstandard approach, Invent. Math. 76 (1984), no. 1, 77–91.
• Laurent Denis , Diophantine geometry on Drinfeld modules, The arithmetic of function fields (Columbus, OH, 1991), 285–302, Ohio State Univ. Math. Res. Inst. Publ., 2, de Gruyter, Berlin, 1992.
• —, \ti{Hauters canoniques et modules de Drinfeld} \jo{Math. Ann.} \vo{294} \yr{1992} \pps{213-223}
• —, \ti{Géométrie et suites récurrentes} \jo{Bull. Soc. Math. France} \vo{122} \yr{1994} \pps{13–27}
• \au{H. Derksen} \ti{A Skolem-Mahler-Lech theorem in positive characteristic and finite automata} \jo{Invent. Math.} \vo{168} \yr{2007} \pps{175–224}
• \au{H. Derksen and D. Masser} \ti{Linear equations over multiplicative groups, recurrences, and mixing I} \jo{Proc. London Math. Soc.} \vo{104} \yr{2012} \pps{1045–1083}
• J. Diller and C. Favre, Dynamics of bimeromorphic maps of surfaces, Amer. J. Math. 123 (2001), 1135–1169.
• A. Douady and J. H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993), 263–297.
• R. Dujardin and C. Favre, The dynamical Manin-Mumford problem for plane polynomial automorphisms, preprint.
• J.-H. Evertse, The number of solutions of decomposable form equations Invent. Math. 122 (1995), 559–601.
• \au{ J.-H. Evertse, H. P. Schlickewei, and W. M. Schmidt} \ti{Linear equations in variables which lie in a multiplicative group} \jo{Ann. of Math. (2)} \vo{155} \yr{2002} \pps{807–836}
• X. Faber and A. Granville, Prime factors of dynamical sequences, J. Reine Angew. Math. 661 (2011), 189–214.
• N. Fakhruddin, The algebraic dynamics of generic endomorphisms of $\bP ^n$, Algebra & Number Theory 8 (2014), no. 3, 587–608.
• \au{G. Faltings} \ti{Endlichkeitssätze für abelsche Varietäten über Zahlkörpern} \jo{Ivent. Math.} \vo{73} \yr{1983} \pps{349–366}
• —, Diophantine approximation on abelian varieties, Ann. of Math. (2) 133 (1991), no. 3, 549–576.
• —, \ti{The general case of S. Lang’s conjecture} Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), 175–182, Perspect. Math. 15, Academic Press, San Diego, CA, 1994.
• C. Favre, Dynamique des applications rationnelles, PhD thesis, Université Paris-Sud XI - Orsay, 2000.
• \au{C. Favre and M. Jonsson} \ti{Dynamical compactification of $\C ^2$} \jo{Ann. Math. (2)} \vo{173} \yr{2011} \pps{211–248}
• C. Favre and J. Rivera-Letelier, Équidistribution quantitative des points de petite hauteur sur la droite projective, Math. Ann. 335 (2006), 311–361.
• H. Furstenberg, Poincaré recurrence and number theory, Bull. Amer. Math. Soc. 5 (1981), 211–234.
• \au{D. Ghioca} \ti{The Mordell-Lang theorem for Drinfeld modules} \jo{Int. Math. Res. Not. IMRN} \vo{53} \yr{2005} \pps{3273–3307}
• —, \ti{Equidistribution for torsion points of Drinfeld modules} \jo{Math. Ann.} \vo{336} \yr{2006} \pps{841–865}
• —, \ti{Mordell exceptional locus for subvarieties of the additive group} \jo{Math. Res. Lett.} \vo{15} \yr{2008} \pps{43–50}
• —, \ti{The isotrivial case in the Mordell-Lang Theorem} \jo{Tran. Amer. Math. Soc.} \vo{360} \yr{2008} \pps{3839–3856}
• —, \ti{Towards the full Mordell-Lang conjecture for Drinfeld modules} \jo{Canad. Math. Bull.} \vo{53} \yr{2010} \pps{95–101}
• —, Integral points for Drinfeld modules, J. Number Theory 140 (2014), 93–121.
• \au{D. Ghioca and L.-C. Hsia} \ti{Torsion points in families of Drinfeld modules} \jo{Acta Arith.} \yr{2013} \vo{161} \pps{219–240}
• \au{D. Ghioca, L.-C. Hsia, and T. J. Tucker} \ti{Preperiodic points for families of polynomials} \jo{Algebra & Number Theory} \yr{2013} \vo{7} \pps{701–732}
• —, \ti{Preperiodic points for families of rational maps} \jo{Proc. London Math. Soc. (3)} \vo{110} \yr{2015} no. 2, \pps{395–427}
• —, Unlikely intersection for two-parameter families of polynomials, Int. Math. Res. Not. IMRN to appear.
• \au{D. Ghioca and R. Moosa} \ti{Division points on subvarieties of semiabelian varieties} \jo{IMRN} \vo{19} \yr{2006} \pps{1–23}
• D. Ghioca, K. Nguyen, and T. J. Tucker, Portraits of preperiodic points under rational maps, Math. Proc. Cambridge Philos. Soc. 159 (2015), no. 1, 165–186.
• \au{D. Ghioca and T. Scanlon} \ti{Algebraic equations on the adélic closure of a Drinfeld module} \jo{Israel J. Math.} \vo{194} \yr{2013} \pps{461–483}
• —, \ti{Density of orbits of endomorphisms of abelian varieties} \jo{Tran. Amer. Math. Soc.} to appear.
• \au{D. Ghioca and T. J. Tucker} \ti{Equidistribution and integral points for Drinfeld modules} \jo{Trans. Amer. Math. Soc.} \vo{360} \yr{2008} \pps{4863–4887}
• —, \ti{A dynamical version of the Mordell-Lang conjecture for the additive group} \jo{Compositio Math.} \vo{164} \yr{2008} \pps{304–316}
• —, \ti{Periodic points, linearizing maps, and the dynamical Mordell-Lang problem} \jo{J. Number Theory} \vo{129} \yr{2009} \pps{1392–1403}
• —, \ti{Proof of a dynamical Bogomolov conjecture for lines under polynomial actions} \jo{Proc. Amer. Math. Soc.} \vo{138} \yr{2010} \pps{937–942}
• \au{D. Ghioca, T. J. Tucker and S. Zhang} \ti{Towards a dynamical Manin-Mumford Conjecture} \jo{Int. Math. Res. Not. IMRN} 2011, no. 22, 5109–5122.
• \au{D. Ghioca, T. J. Tucker, and M. E. Zieve} \ti{Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture} \jo{Invent. Math.} \vo{171} \yr{2008} \pps{463–483}
• —, \ti{The Mordell-Lang question for endomorphisms of semiabelian varieties} \jo{J. Theor. Nombres Bordeaux} \vo{23} \yr{2011} \pps{645–666}
• —, \ti{Linear relations between polynomial orbits} \jo{Duke Math. J.} \yr{2012} \vo{161} \pps{1379–1410}
• W. Gignac, Equidistribution of preimages in nonarchimedean dynamics, PhD thesis, University of Michigan, 2013.
• —, Measures and dynamics on Noetherian spaces, J. Geom. Anal. 24 (2014), no. 4, 1770–1793.
• \au{D. Goss} \ti{Basic Structure of Function field Arithmetic} Springer-Verlag, Berlin, 1996.
• \au{U. Görtz and T. Wedhorn} \ti{Algebraic geometry I. Schemes with examples and exercises} Advanced Lectures in Mathematics. Vieweg + Teubner, Wiesbaden, 2010. viii+615 pp.
• D. Grant and S.-I. Ih, Integral division points on curves, Compos. Math. 149 (2013), no. 12, 2011–2035.
• C. Gratton, K. Nguyen, and T. J. Tucker, $ABC$ implies primitive prime divisors in arithmetic dynamics, Bull. London Math. Soc. 45 (2013), no. 6, 1194–1208.
• \au{S. Häberli} \ti{Kummer theory of Drinfeld modules} Master’s Thesis, ETH Zürich, May 2011.
• \au{P. Habegger} \ti{Intersecting subvarieties of abelian varieties with algebraic subgroups of complementary dimension} \jo{Invent. Math.} \vo{176} \yr{2009} \pps{405–447}
• \au{G. af Hällström} \ti{Über halbvertauschbare Polynome} \jo{Acta Acad. Abo.} \vo{21} \yr{1957} no. 2, 20 pp.
• S. Hamblen, R. Jones, and K. Madhu, The density of primes in orbits of $z^d + c$, Int. Math. Res. Not., 2015(7):1924-1958.
• R. Hartshorne, Algebraic geometry, Springer-Verlag, New York, 1977.
• J. Heintz, Definability and fast quantifier elimination in algebraically closed fields, Theoret. Comput. Sci. 24 (1983), no. 3, 239–277.
• M. Herman and J.-C. Yoccoz, Generalizations of some theorems of small divisors to non-archimedean fields, Geometric dynamics (Rio de Janeiro, 1981), Lecture Notes in Math., no. 1007, Springer-Verlag, Berlin, 1983, pp. 408–447.
• M. Hindry, Autour d’une conjecture de Serge Lang, Invent. Math. 94 (1988), 575–603.
• M. Hindry and J. H. Silverman, Diophantine geometry. An introduction, Graduate Texts in Mathematics 201. Springer-Verlag, New York, 2000. xiv+558 pp
• \au{E. Hrushovski} \ti{The Mordell-Lang conjecture for function fields} \jo{J. Amer. Math. Soc.} \vo{9} \yr{1996} \pps{667–690}
• —, \ti{Proof of Manin’s theorem by reduction to positive characteristic} \pps{197–205} Model Theory and Algebraic Geometry, Lecture Notes in Mathematics 1696, Elisabeth Bouscaren (Ed.), 1999.
• B. Hutz, Good reduction of periodic points on projective varieties, Illinois J. Math. 53 (2009), 1109–1126.
• S. Iitaka, Logarithmic forms of algebraic varieties, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), no. 3, 525–544.
• P. Ingram and J. H. Silverman, Primitive divisors in arithmetic dynamics, Math. Proc. Cambridge Philos. Soc. 146 (2009), 289–302.
• J. Jost, Riemannian geometry and geometric analysis, third ed., Universitext, Springer-Verlag, Berlin, 2002.
• S. Kawaguchi and J. H. Silverman, Examples of dynamical degree equals arithmetic degree, Michigan Math. J. 63 (2014), no. 1, 41–63.
• \au{D. S. Keeler, D. Rogalski, and J.T. Stafford} \ti{Naïve noncommutative blowing up} \jo{Duke Math. J.} \vo{126} \yr{2005} \pps{491–546}
• R. Jones, The density of prime divisors in the arithmetic dynamics of quadratic polynomials, J. Lond. Math. Soc. (2) 78 (2008), no. 2, 523–544.
• R. Jones, Galois representations from pre-image trees: an arboreal survey, Pub. Math. Besançon. (2013), 107–136
• —, Fixed-point-free elements of iterated monodromy groups, Trans. Amer. Math. Soc., 367(3):2023-2049, 2015.
• R. Jones, J. Cahn, and J. Spear, Powers in orbits of rational functions: cases of an arithmetic dynamical Mordell-Lang conjecture, in preparation.
• J. Juul, P. Kurlberg, K. Madhu, and T. J. Tucker, Wreath products and proportions of periodic points, to appear in Int. Math. Res. Not. IMRN.
• \au{S. Lang} \ti{Integral points on curves} \jo{Publ. Math. IHES} \vo{6} \yr{1960} \pps{27–43}
• —, \ti{Fundamentals of Diophantine geometry} Springer-Verlag, New York, 1983.
• —, Algebra, third ed., Springer-Verlag, New York, 2002, xvi+914 pp.
• M. Laurent, Equations diophantiennes exponentielles, Invent. Math. 78 (1984), 299–327.
• \au{C. Lech} \ti{A note on recurring series} \jo{Ark. Mat.} \vo{2} \yr{1953} \pps{417–421}
• A. Levin, The exceptional set in Vojta’s conjecture for algebraic points of bounded degree, Proc. Amer. Math. Soc. 140 (2012), no. 7, 2267–2277.
• A. Levin and Y. Yasufuku Integral points and orbits of endomorphisms on the projective plane, preprint.
• \au{K. Mahler} \ti{Eine arithmetische Eigenshaft der Taylor-Koeffizienten rationaler Funktionen} \jo{Proc. Kon. Ned. Akad. Wetensch.} \vo{38} \yr{1935} \pps{50–60}
• —, An interpolation series for continuous functions of a $p$-adic variable, J. Reine Angew. Math. 199 (1958), 23–34.
• —, A correction to the paper “an interpolation series for continuous functions of a $p$-adic variable”, J. Reine Angew. Math. 208 (1961), 70–72.
• \au{D. Masser and U. Zannier} \ti{Torsion anomalous points and families of elliptic curves} \jo{C. R. Math. Acad. Sci. Paris} \vo{346} \yr{2008} \pps{491–494}
• —\ti{Torsion anomalous points and families of elliptic curves} \jo{Amer. J. Math.} \vo{132} \yr{2010} \pps{1677–1691}
• —\ti{Torsion points on families of squares of elliptic curves} Math. Ann. 352 (2012), 453–484.
• H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986, Translated from the Japanese by M. Reid.
• A. Medvedev, Minimal sets in $ACFA$, PhD thesis, UC Berkeley, 2007.
• A. Medvedev and T. Scanlon, Invariant varieties for polynomial dynamical systems, Ann. Math. (2) 179 (2014), no. 1, 81–177.
• \au{C. Methfessel} \ti{On the zeros of recurrence sequences with non-constant coefficients} \jo{Arch. Math. (Basel)} \vo{74} \yr{2000} \pps{201–206}
• \au{R. Moosa and T. Scanlon} \ti{The Mordell-Lang Conjecture in positive characteristic revisited} Model Theory and Applications (eds. L. Bélair, P. D’Aquino, D. Marker, M. Otero, F. Point, & A. Wilkie), 2003, 273–296.
• —\ti{$F$-structures and integral points on semiabelian varieties over finite fields} \jo{Amer. J. Math.} \vo{126} \yr{2004} \pps{473–522}
• P. Morton and J. H. Silverman, Rational periodic points of rational functions, Internat. Math. Res. Notices (1994), no. 2, 97–110.
• —, Periodic points, multiplicities, and dynamical units, J. Reine Angew. Math. 461 (1995), 81–122.
• D. Mumford, A remark on Mordell’s conjecture, Amer. J. Math. 87 (1965), 1007–1016.
• \au{P. Müller and M. E. Zieve} \ti{On Ritt’s polynomial decomposition theorems} submitted for publication.
• V. Nekrashevych, Self-similar groups, volume 117 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2005.
• T. W. Ng and M.-X. Wang, Ritt’s theory on the unit disk, Forum Math. 25 (2013), 821–851.
• K. Nguyen, Some arithmetic dynamics of diagonally split polynomial maps, Int. Math. Res. Not. IMRN, vol. 2015, 1159–1199.
• \au{K. Nguyen and M. E. Zieve} \ti{Algebraic dynamics of split morphisms associated to rational maps having generic ramification} preprint.
• —\ti{Functional equations and the curves $f(X)=g(Y)$ for generic $f$ and arbitrary $g$} preprint.
• R. W. K. Odoni, The Galois theory of iterates and composites of polynomials, Proc. London Math. Soc. (3) 51 (1985), no. 3, 385–414.
• \au{A. Ostafe and M. Sha} \ti{On the quantitative Dynamical Mordell-Lang Conjecture} preprint.
• \au{F. Pazuki} \ti{Zhang’s conjecture and squares of abelian surfaces} \jo{C. R. Math. Acad. Sci. Paris} \yr{2010} \vo{348} \pps{483–486}
• T. Pezda, Cycles of polynomial mappings in several variables over rings of integers in finite extensions of the rationals. II, Monatsh. Math. 145 (2005), no. 4, 321–331.
• C. Petsche, On the distribution of orbits in affine varieties, preprint, \xxx11401.3425.
• J. Pila and U. Zannier, Rational points in periodic analytic sets and the Manin- Mumford conjecture, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008), 149–162.
• A. Pillay, The model-theoretic content of Lang’s conjecture, Model Theory and Algebraic Geometry, Lecture Notes in Math. 1696 (E. Bouscaren, ed.), Springer-Verlag, Berlin, 1998, pp. 101–106.
• J. Piñeiro, L. Szpiro, and T. Tucker, Mahler measure for dynamical systems on $\mathbb {P}^{1}$ and intersection theory on a singular arithmetic surface, Geometric methods in algebra and number theory (F. Bogomolov and Y. Tschinkel, eds.), Progress in Mathematics 235, Birkhäuser, 2004, pp. 219–250.
• \au{R. Pink} \ti{A common generalization of the conjectures of André-Oort, Manin-Mumford, and Mordell-Lang} unpublished manuscript, 2005.
• J. M. Pollard, A Monte Carlo method for factorization, Nordisk Tidskr. Informationsbehandling (BIT) 15 (1975), no. 3, 331–334.
• B. Poonen, Local height functions and the Mordell-Weil theorem for Drinfeld modules, Compositio Math. 97 (1995), 349–368.
• —, $p$-adic interpolation of iterates, Bull. London Math. Soc. 46 (2014), no. 3, 525–527.
• B. Poonen and J. F. Voloch, The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Ann. Math. 171 (2010), 511–532.
• M. Raynaud, Courbes sur une variété abélienne et points de torsion, Invent. Math. 71 (1983), 207–233.
• —, Sous-variétés d’une variété abélienne et points de torsion, Arithmetic and geometry, vol. I, Progr. Math., vol. 35, Birkhäuser, Boston, MA, 1983, pp. 327–352.
• \au{J. F. Ritt} \ti{On the iteration of rational functions} \jo{Trans. Amer. Math. Soc.} \vo{21} \yr{1920} \pps{348–356}
• J. Rivera-Letelier, Dynamique des fonctions rationnelles sur des corps locaux, Astérisque (2003), no. 287, 147–230, Geometric methods in dynamics. II.
• A. M. Robert, A course in $p$-adic analysis, Graduate Texts in Mathematics, vol. 198, Springer-Verlag, New York, 2000.
• L. A. Rubel, Some research problems about algebraic differential equations, Trans. Amer. Math. Soc. 280 (1983), 43–52.
• T. Scanlon, Diophantine geometry of the torsion of a Drinfeld module, J. Number Theory 97 (2002), no. 1, 10–25.
• —, A Euclidean Skolem-Mahler-Lech-Chabauty method, Math. Res. Lett. 18 (2011), 835–842.
• —, Analytic relations on a dynamical orbit, preprint.
• \au{T. Scanlon and Y. Yasufuku} \ti{Exponential-polynomial equations and dynamical return sets} \jo{Int. Math. Res. Not. IMRN} 2014, no. 16, 4357–4367.
• I. R. Shafarevich, Basic algebraic geometry, study ed., Springer-Verlag, Berlin, 1977, Translated from the Russian by K. A. Hirsch, Revised printing of Grundlehren der mathematischen Wissenschaften, Vol. 213, 1974.
• A. Schinzel, Primitive divisors of the expression $a^n-b^n$ in algebraic number fields, J. Reine Angew. Math. 268/269 (1974), 27–33.
• \au{W. M. Schmidt} \ti{The zero multiplicity of linear recurrence sequences} \jo{Acta Math.} \vo{182} \yr{1999} \pps{243–282}
• —\ti{Zeros of linear recurrence sequences} \jo{Publ. Math. Debrecen} \vo{56} \yr{2000} \pps{609–630}
• \au{H. Sharif and C. F. Woodcock} \ti{Algebraic functions over a field of positive characteristic and Hadamard products} \jo{J. London Math. Soc. (2)} \vo{37} \yr{1988} \pps{no. 3, 395–403}
• \au{C. L. Siegel} \ti{Über einige Anwendungen Diophantischer Approximationen} \jo{Abh. Preuss. Akad. Wiss. Phys. Math. Kl.} \yr{1929} \pps{41–69} (Reprinted as pp. 209–266 of his Gesammelte Abhandlungen I, Springer, Berlin, 1966.)
• \au{J. H. Silverman} \ti{Heights and the specialization map for families of abelian varieties} \jo{J. Reine Angew. Math.} \vo{342} \yr{1983} \pps{197–211}
• —, \ti{Integer points, Diophantine approximation, and iteration of rational maps} \jo{Duke Math. J.} \vo{71} \yr{1993} \pps{793–829}
• —, The arithmetic of dynamical systems, Graduate Texts in Mathematics 241, Springer, New York, 2007, x+511 pp.
• —, Variation of periods modulo p in arithmetic dynamics, New York J. Math. 14 (2008), 601–616.
• —, Primitive divisors, dynamical Zsigmondy sets, and Vojta’s conjecture, J. Number Theory 133 (2013), no. 9, 2948–2963.
• J. H. Silverman and B. Viray, On a uniform bound for the number of exceptional linear subvarieties in the Mordell-Lang conjecture, Math. Res. Lett. 20 (2013), no. 3, 547–566.
• J. H. Silverman and J. F. Voloch, A Local-Global Criterion for Dynamics on $\bP ^1$, Acta Arith. 137 (2009), 285–294.
• \au{T. Skolem} \ti{Ein Verfahren zur Behandlung gewisser exponentialer Gleichungen und diophantischer Gleichungen} Comptes Rendus Congr. Math. Scand. (Stockholm, 1934) 163–188.
• \au{V. Sookdeo} \ti{Integer points in backward orbits} J. Number Theory 131 (2011), 1229–1239.
• \au{V. Srinivas} \ti{On the embedding dimension of an affine variety} \jo{Math. Ann.} \yr{1991} \vo{289} \pps{125–132}
• \au{P. Stevenhagen and H. W. Lenstra Jr.} \ti{Chebotarev and his density theorem} \jo{Math. Intelligencer} \vo{18} \yr{1996} \pps{26–37}
• M. Stoll, Galois groups over $\textbf {Q}$ of some iterated polynomials, Arch. Math. (Basel) 59 (1992), no. 3, 239–244.
• C.-L. Sun, Adélic points of subvarieties of isotrivial semi-abelian varieties over a global field of positive characteristic, preprint, \xxx1005.4998
• \au{E. Szemerédi} \ti{On sets of integers containing no $k$ elements in arithmetic progression} \jo{Acta Arithm.} \vo{27} \yr{1975} \pps{199–245}
• L. Szpiro, E. Ullmo, and S. Zhang, Équirépartition des petits points (French) [Uniform distribution of small points], Invent. Math. 127 (1997), 337–347.
• E. Ullmo, Positivité et discrétion des points algébriques des courbes, Ann. of Math. (2) 147 (1998), 167–179.
• T. J. Tucker, Integer points in arithmetic sequences, Bull. Inst. Math. Acad. Sin. (N.S.) 9 (2014), no. 4, 633–639.
• P. Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987.
• —\ti{Mordell’s conjecture over function fields} \jo{Invent. Math.} \vo{98} \yr{1989} \pps{115–138}
• —\ti{Integral points on subvarieties of semiabelian varieties. I} \jo{Invent. Math.} \vo{126} \yr{1996} \pps{133–181}
• —, Integral points on subvarieties of semiabelian varieties. II, Amer. J. Math. 121 (1999), no. 2, 283–313.
• M. Wang, Endomorphisms of uniformization spaces, preprint.
• A. J. Wilkie, Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function J. Amer. Math. Soc. 9 (1996), 1051–1094.
• J. Xie, Dynamical Mordell-Lang Conjecture for birational polynomial morphisms on $\bA ^2$, Math. Ann. 360 (2014), no. 1-2, 457–480.
• —, Intersection of valuation rings in $k[x,y]$, preprint available on \xxx{1403.6052}
• —, The Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane, preprint available on \xxx{1503.00773}
• Y Yasufuku, Vojta’s conjecture and dynamics, Algebraic number theory and related topics 2009, RIMS Kôkyûroku Bessatsu, B25, Res. Inst. Math. Sci. (RIMS), Kyoto, 2011, pp. 75–86.
• —, Deviations from $S$-integrality in orbits on $\mathbb {P}^N$, Bull. Inst. Math. Acad. Sin. (N.S.) 9 (2014), no. 4, 603–631.
• —, Integral points and relative sizes of coordinates of orbits in $\mathbb {P}^N$, Math. Z. 279 (2015), no. 3-4, 1121–1141.
• K. Yu, Linear forms in $p$-adic logarithms. II, Compositio Math. 74 (1990), 15–113.
• X. Yuan, Big line bundles over arithmetic varieties, Invent. Math. 173 (2008), 603–649.
• X. Yuan and S.-W. Zhang, Calabi theorem and algebraic dynamics, preprint, 23 pages.
• U. Zannier, Lecture notes on Diophantine analysis, Appunti. Scuola Normale Superiore di Pisa (Nuova Serie) [Lecture Notes. Scuola Normale Superiore di Pisa (New Series)], vol. 8, Edizioni della Normale, Pisa, 2009, With an appendix by Francesco Amoroso.
• —, Some problems of unlikely intersections in arithmetic and geometry, Annals of Mathematics Studies, vol. 181, Princeton University Press, Princeton, NJ, 2012, With appendixes by David Masser.
• S. Zhang, Small points and adelic metrics, J. Algebraic Geometry 4 (1995), 281–300.
• —, Equidistribution of small points on abelian varieties, Ann. of Math. (2) 147 (1998), 159–165.
• —, Distributions in algebraic dynamics, Survey in Differential Geometry, vol. 10, International Press, 2006, pp. 381–430.
• M. E. Zieve, Cycles of polynomial mappings, PhD thesis, University of California at Berkeley, 1996
• —, Decompositions of Laurent polynomials, preprint.
• K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math. Phys. 3 (1892) 265–284.

\newcommand{\au}[1]#1, \newcommand{\ti}[1]#1, \newcommand{\jo}[1]#1 \newcommand{\vo}[1]#1 \newcommand{\yr}[1](#1), \newcommand{\page}[1]#1. \newcommand{\ppx}[1]#1, \newcommand{\pps}[1]#1. \newcommand{\bk}[1]#1, \newcommand{\inbk}[1]in: #1 \newcommand{\xxx}[1]arXiv:#1.

• M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, Dover Publications Inc., New York, 1992, Reprint of the 1972 edition.
• B. Adamczewski and J. P. Bell, On vanishing coefficients of algebraic power series over fields of positive characteristic. Invent. Math. 187 (2012), 343–393.
• A. Akbary and D. Ghioca, Periods of orbits modulo primes, J. Number Theory 129 (2009), 2831–2842.
• J.-P. Allouche and J. Shallit, Automatic sequences. Theory, applications, generalizations. Cambridge University Press, Cambridge, 2003.
• A. Altman and S. Kleiman, Introduction to Grothendieck duality theory, Lecture Notes in Mathematics, Vol. 146, Springer-Verlag, Berlin, 1970.
• E. Amerik, Existence of non-preperiodic algebraic points for a rational self-map of infinite order, Math. Res. Lett. 18 (2011), 251–256.
• E. Amerik, F. Bogomolov, and M. Rovinsky, Remarks on endomorphisms and rational points, Compositio Math. 147 (2011), 1819–1842.
• E. Amerik and F. Campana, Fibrations méromorphes sur certaines variétés à fibré canonique trivial, Pure Appl. Math. Q. 4 (2008), 509–545.
• M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
• P. Autissier, Points entiers sur les surfaces arithmétiques, J. reine. angew. Math 531 (2001), 201–235.
• E. Bach, Toward a theory of Pollard’s rho method, Inform. and Comput. 90 (1991), 139–155.
• \au{M. Baker} \ti{A finiteness theorem for canonical heights attached to rational maps over function fields} \jo{J. Reine Angew. Math.} \vo{626} \yr{2009} \pps{205–233}
• \au{M. Baker and L. DeMarco} \ti{Preperiodic points and unlikely intersections} \jo{Duke Math. J.} \vo{159} \yr{2011} \pps{1–29}
• —, \ti{Special curves and post-critically-finite polynomials} \jo{Forum Math. $\pi$} \vo{1} \yr{2013} \pps{e3, 35 pp}
• \au{M. Baker and L.-C. Hsia} \ti{Canonical heights, transfinite diameters, and polynomial dynamics} \jo{J. reine angew. Math.} \vo{585} \yr{2005} \pps{61–92}
• M. Baker, S.-I. Ih, and R. Rumely, A finiteness property of torsion points, Algebra Number Theory 2 (2008), no. 2, 217–248.
• M. Baker and R. Rumely, Equidistribution of small points, rational dynamics, and potential theory, Ann. Inst. Fourier (Grenoble) 56 (2006), 625–688.
• —, \ti{Potential theory and dynamics on the Berkovich projective line} Mathematics Surveys and Monographs 159, American Mathematical Society, Providence, RI, 2010.
• A. S. Bang, Taltheoretiske Undersogelse, Tidsskrift Mat. 4 (1886), 70–80, 130–137.
• \au{A. Beardon} \ti{Iteration of rational functions} Complex analytic dynamical systems. Graduate Texts in Mathematics 132. Springer-Verlag, New York, 1991.
• J. P. Bell, A generalized Skolem-Mahler-Lech theorem for affine varieties, J. London Math. Soc. (2) 73 (2006), 367–379.
• J. P. Bell, S. N. Burris, K. Yeats, On the set of zero coefficients of a function satisfying a linear differential equation, Math. Proc. Cambridge Philos. Soc. 153 (2012), 235–247.
• J. P. Bell, D. Ghioca, and T. J. Tucker, The dynamical Mordell-Lang problem for étale maps, Amer. J. Math. 132 (2010), 1655–1675.
• —, Applications of $p$-adic analysis for bounding periods of subvarieties under étale maps, Int. Math. Res. Not. IMRN, vol. 2015, 3576–3597.
• —, The Dynamical Mordell-Lang problem for Noetherian spaces, Funct. Approx. Comm. Math. 53 (2015), no. 2, 313–328.
• J. P. Bell, D. Ghioca, and Z. Reichstein, On a dynamical variant of a theorem of Rosenlicht, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) to appear.
• J. P. Bell and J. Lagarias, A Skolem-Mahler-Lech theorem for iterated automorphisms of $K$-algebras, Canad. J. Math. 67 (2015), no. 2, 286–314.
• \au{R. L. Benedetto} \ti{Heights and preperiodic points for polynomials over function fields} \jo{Int. Math. Res. Not.} \vo{62} \yr{2005} \pps{3855–3866}
• \au{R. L. Benedetto, D. Ghioca, P. Kurlberg, and T. J. Tucker} \ti{A gap principle for dynamics} \jo{Compositio Math.} \yr{2010} \vo{146} \pps{1056–1072}
• —, A case of the dynamical Mordell-Lang conjecture (with an Appendix by U. Zannier), Math. Ann. 352 (2012), 1–26.
• \au{R. L. Benedetto, D. Ghioca, B. A. Hutz, P. Kurlberg, T. Scanlon, and T. J. Tucker} \ti{Periods of rational maps modulo primes} \jo{Math. Ann.} \vo{355} \yr{2013} \pps{637–660}
• M. Bennett, Y. Bugeaud, and M. Mignotte, Perfect powers with few binary digits and related Diophantine problems, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 12 (2013), no. 4, 941–953.
• \au{V. Berkovich} \ti{Spectral theory and analytic geometry over non-Archimedean fields} Mathematical Surveys and Monographs 33, American Mathematical Society, Providence, RI, 1990.
• \au{F. Beukers and H. P. Schlickewei} \ti{The equation $x+y=1$ in finitely generated groups} \jo{Acta Arith.} \vo{78} \yr{1996} \pps{189–199}
• \au{J.-P. Bézivin} \ti{Une généralisation du théorème de Skolem-Mahler-Lech} \jo{Quart. J. Math. Oxford Ser. (2)} \vo{40} \yr{1989} \pps{133–138}
• \au{Y. F. Bilu and R. F. Tichy} \ti{The Diophantine equation $f(x)=g(y)$} \jo{Acta Arith.} \vo{95} \yr{2000} \pps{261–288}
• E. Bombieri and W. Gubler, Heights in Diophantine geometry, New Mathematical Monographs, vol. 4, Cambridge University Press, Cambridge, 2006.
• \au{E. Bombieri, D. Masser, and U. Zannier} \ti{Intersecting a curve with algebraic subgroups of multiplicative groups} \jo{IMRN} \vo{20} \yr{1999} \pps{1119–1140}
• A. I. Borevich and I. R. Shafarevich, Number theory, Translated from the Russian by Newcomb Greenleaf. Pure and Applied Mathematics, Vol. 20, Academic Press, New York, 1966.
• V. Bosser, Minorations de formes linéaires de logarithmes pour les modules de Drinfeld, J. Number Theory 75 (1999), no. 2, 279–323.
• N. Bourbaki, Lie groups and Lie algebras. Chapters 1–3, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1998, Translated from the French, Reprint of the 1989 English translation.
• —, Éléments de mathématique. Algèbre commutative. Chapitres 8 et 9, Springer, Berlin, 2006, Reprint of the 1983 original.
• \au{B. Branner and J. H. Hubbard} \ti{The iteration of cubic polynomials. I. The global topology of parameter space.} \jo{Acta Math.} \vo{160(3-4)} \yr{1988} \pps{143-206}
• X. Buff, A. L. Epstein, and S. Koch, Böttcher coordinates, Indiana Univ. Math. J. 61 (2012), no. 5, 1765–1799.
• \au{G. S. Call and J. H. Silverman} \ti{Canonical heights on varieties with morphisms} \jo{Compositio Math.} \vo{89} \yr{1993} \pps{163–205}
• \au{L. Carleson and T. W. Gamelin} \ti{Complex dynamics} Springer-Verlag, New York, 1993.
• C. Chabauty, Sur les points rationnels des courbes algébriques de genre supérieur à l’unité, C. R. Acad. Sci. Paris 212 (1941), 882–885.
• A. Chambert-Loir, Mesures et équidistribution sur les espaces de Berkovich, J. Reine Angew. Math. 595 (2006), 215–235.
• Z. Chatzidakis and E. Hrushovski, Difference fields and descent in algebraic dynamics. I, J. Inst. Math. Jussieu 7 (2008), 635–686.
• —, Difference fields and descent in algebraic dynamics. II, J. Inst. Math. Jussieu 7 (2008), 687–704.
• R. F. Coleman, Effective Chabauty, Duke Math. J. 52 (1985), no. 3, 765–770.
• P. Corvaja and U. Zannier, On the Diophantine equation $f(a^m, y) = b^n$, Acta Arith. 94 (2000), 25–40.
• P. Corvaja and U. Zannier, Finiteness of odd perfect powers with four nonzero binary digits, Ann. Inst. Fourier (Grenoble) 63 (2013), no. 2, 715–731.
• P. Corvaja, V. Sookdeo, T. J. Tucker, and U. Zannier, Integral points in two-parameter orbits, J. Reine Angew. Math., to appear.
• S. D. Cutkosky and V. Srinivas, On a problem of Zariski on dimensions of linear systems, Ann. of Math. (2) 137 (1993), no. 3, 531–559.
• H. Davenport and K. F. Roth, Rational approximations to algebraic numbers, Mathematika 2 (1955), 160–167.
• P. Deligne, La Conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273–307.
• L. Demangos, Some examples toward a Manin-Mumford conjecture for abelian uniformizable $T$-modules, preprint.
• L. DeMarco, X. Wang, and H. Ye, Torsion points and the Lattes family, to appear in Amer. J. Math.
• L. van den Dries and A. Günaydin, The fields of real and complex numbers with a small multiplicative group, Proc. London Math. Soc. 93 (2006), 43–81.
• L. van den Dries, A. Macintyre, and D. Marker, the elementary theory of restricted analytic fields with exponentiation, Ann. Math. 140 (1994), 183–205.
• L. van den Dries and C. Miller, On the real exponential field with restricted analytic functions Israel J. Math. 85 (1994), 19–56.
• L. van den Dries and K. Schmidt, Bounds in the theory of polynomial rings over fields. A nonstandard approach, Invent. Math. 76 (1984), no. 1, 77–91.
• Laurent Denis , Diophantine geometry on Drinfeld modules, The arithmetic of function fields (Columbus, OH, 1991), 285–302, Ohio State Univ. Math. Res. Inst. Publ., 2, de Gruyter, Berlin, 1992.
• —, \ti{Hauters canoniques et modules de Drinfeld} \jo{Math. Ann.} \vo{294} \yr{1992} \pps{213-223}
• —, \ti{Géométrie et suites récurrentes} \jo{Bull. Soc. Math. France} \vo{122} \yr{1994} \pps{13–27}
• \au{H. Derksen} \ti{A Skolem-Mahler-Lech theorem in positive characteristic and finite automata} \jo{Invent. Math.} \vo{168} \yr{2007} \pps{175–224}
• \au{H. Derksen and D. Masser} \ti{Linear equations over multiplicative groups, recurrences, and mixing I} \jo{Proc. London Math. Soc.} \vo{104} \yr{2012} \pps{1045–1083}
• J. Diller and C. Favre, Dynamics of bimeromorphic maps of surfaces, Amer. J. Math. 123 (2001), 1135–1169.
• A. Douady and J. H. Hubbard, A proof of Thurston’s topological characterization of rational functions, Acta Math. 171 (1993), 263–297.
• R. Dujardin and C. Favre, The dynamical Manin-Mumford problem for plane polynomial automorphisms, preprint.
• J.-H. Evertse, The number of solutions of decomposable form equations Invent. Math. 122 (1995), 559–601.
• \au{ J.-H. Evertse, H. P. Schlickewei, and W. M. Schmidt} \ti{Linear equations in variables which lie in a multiplicative group} \jo{Ann. of Math. (2)} \vo{155} \yr{2002} \pps{807–836}
• X. Faber and A. Granville, Prime factors of dynamical sequences, J. Reine Angew. Math. 661 (2011), 189–214.
• N. Fakhruddin, The algebraic dynamics of generic endomorphisms of $\bP ^n$, Algebra & Number Theory 8 (2014), no. 3, 587–608.
• \au{G. Faltings} \ti{Endlichkeitssätze für abelsche Varietäten über Zahlkörpern} \jo{Ivent. Math.} \vo{73} \yr{1983} \pps{349–366}
• —, Diophantine approximation on abelian varieties, Ann. of Math. (2) 133 (1991), no. 3, 549–576.
• —, \ti{The general case of S. Lang’s conjecture} Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), 175–182, Perspect. Math. 15, Academic Press, San Diego, CA, 1994.
• C. Favre, Dynamique des applications rationnelles, PhD thesis, Université Paris-Sud XI - Orsay, 2000.
• \au{C. Favre and M. Jonsson} \ti{Dynamical compactification of $\C ^2$} \jo{Ann. Math. (2)} \vo{173} \yr{2011} \pps{211–248}
• C. Favre and J. Rivera-Letelier, Équidistribution quantitative des points de petite hauteur sur la droite projective, Math. Ann. 335 (2006), 311–361.
• H. Furstenberg, Poincaré recurrence and number theory, Bull. Amer. Math. Soc. 5 (1981), 211–234.
• \au{D. Ghioca} \ti{The Mordell-Lang theorem for Drinfeld modules} \jo{Int. Math. Res. Not. IMRN} \vo{53} \yr{2005} \pps{3273–3307}
• —, \ti{Equidistribution for torsion points of Drinfeld modules} \jo{Math. Ann.} \vo{336} \yr{2006} \pps{841–865}
• —, \ti{Mordell exceptional locus for subvarieties of the additive group} \jo{Math. Res. Lett.} \vo{15} \yr{2008} \pps{43–50}
• —, \ti{The isotrivial case in the Mordell-Lang Theorem} \jo{Tran. Amer. Math. Soc.} \vo{360} \yr{2008} \pps{3839–3856}
• —, \ti{Towards the full Mordell-Lang conjecture for Drinfeld modules} \jo{Canad. Math. Bull.} \vo{53} \yr{2010} \pps{95–101}
• —, Integral points for Drinfeld modules, J. Number Theory 140 (2014), 93–121.
• \au{D. Ghioca and L.-C. Hsia} \ti{Torsion points in families of Drinfeld modules} \jo{Acta Arith.} \yr{2013} \vo{161} \pps{219–240}
• \au{D. Ghioca, L.-C. Hsia, and T. J. Tucker} \ti{Preperiodic points for families of polynomials} \jo{Algebra & Number Theory} \yr{2013} \vo{7} \pps{701–732}
• —, \ti{Preperiodic points for families of rational maps} \jo{Proc. London Math. Soc. (3)} \vo{110} \yr{2015} no. 2, \pps{395–427}
• —, Unlikely intersection for two-parameter families of polynomials, Int. Math. Res. Not. IMRN to appear.
• \au{D. Ghioca and R. Moosa} \ti{Division points on subvarieties of semiabelian varieties} \jo{IMRN} \vo{19} \yr{2006} \pps{1–23}
• D. Ghioca, K. Nguyen, and T. J. Tucker, Portraits of preperiodic points under rational maps, Math. Proc. Cambridge Philos. Soc. 159 (2015), no. 1, 165–186.
• \au{D. Ghioca and T. Scanlon} \ti{Algebraic equations on the adélic closure of a Drinfeld module} \jo{Israel J. Math.} \vo{194} \yr{2013} \pps{461–483}
• —, \ti{Density of orbits of endomorphisms of abelian varieties} \jo{Tran. Amer. Math. Soc.} to appear.
• \au{D. Ghioca and T. J. Tucker} \ti{Equidistribution and integral points for Drinfeld modules} \jo{Trans. Amer. Math. Soc.} \vo{360} \yr{2008} \pps{4863–4887}
• —, \ti{A dynamical version of the Mordell-Lang conjecture for the additive group} \jo{Compositio Math.} \vo{164} \yr{2008} \pps{304–316}
• —, \ti{Periodic points, linearizing maps, and the dynamical Mordell-Lang problem} \jo{J. Number Theory} \vo{129} \yr{2009} \pps{1392–1403}
• —, \ti{Proof of a dynamical Bogomolov conjecture for lines under polynomial actions} \jo{Proc. Amer. Math. Soc.} \vo{138} \yr{2010} \pps{937–942}
• \au{D. Ghioca, T. J. Tucker and S. Zhang} \ti{Towards a dynamical Manin-Mumford Conjecture} \jo{Int. Math. Res. Not. IMRN} 2011, no. 22, 5109–5122.
• \au{D. Ghioca, T. J. Tucker, and M. E. Zieve} \ti{Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture} \jo{Invent. Math.} \vo{171} \yr{2008} \pps{463–483}
• —, \ti{The Mordell-Lang question for endomorphisms of semiabelian varieties} \jo{J. Theor. Nombres Bordeaux} \vo{23} \yr{2011} \pps{645–666}
• —, \ti{Linear relations between polynomial orbits} \jo{Duke Math. J.} \yr{2012} \vo{161} \pps{1379–1410}
• W. Gignac, Equidistribution of preimages in nonarchimedean dynamics, PhD thesis, University of Michigan, 2013.
• —, Measures and dynamics on Noetherian spaces, J. Geom. Anal. 24 (2014), no. 4, 1770–1793.
• \au{D. Goss} \ti{Basic Structure of Function field Arithmetic} Springer-Verlag, Berlin, 1996.
• \au{U. Görtz and T. Wedhorn} \ti{Algebraic geometry I. Schemes with examples and exercises} Advanced Lectures in Mathematics. Vieweg + Teubner, Wiesbaden, 2010. viii+615 pp.
• D. Grant and S.-I. Ih, Integral division points on curves, Compos. Math. 149 (2013), no. 12, 2011–2035.
• C. Gratton, K. Nguyen, and T. J. Tucker, $ABC$ implies primitive prime divisors in arithmetic dynamics, Bull. London Math. Soc. 45 (2013), no. 6, 1194–1208.
• \au{S. Häberli} \ti{Kummer theory of Drinfeld modules} Master’s Thesis, ETH Zürich, May 2011.
• \au{P. Habegger} \ti{Intersecting subvarieties of abelian varieties with algebraic subgroups of complementary dimension} \jo{Invent. Math.} \vo{176} \yr{2009} \pps{405–447}
• \au{G. af Hällström} \ti{Über halbvertauschbare Polynome} \jo{Acta Acad. Abo.} \vo{21} \yr{1957} no. 2, 20 pp.
• S. Hamblen, R. Jones, and K. Madhu, The density of primes in orbits of $z^d + c$, Int. Math. Res. Not., 2015(7):1924-1958.
• R. Hartshorne, Algebraic geometry, Springer-Verlag, New York, 1977.
• J. Heintz, Definability and fast quantifier elimination in algebraically closed fields, Theoret. Comput. Sci. 24 (1983), no. 3, 239–277.
• M. Herman and J.-C. Yoccoz, Generalizations of some theorems of small divisors to non-archimedean fields, Geometric dynamics (Rio de Janeiro, 1981), Lecture Notes in Math., no. 1007, Springer-Verlag, Berlin, 1983, pp. 408–447.
• M. Hindry, Autour d’une conjecture de Serge Lang, Invent. Math. 94 (1988), 575–603.
• M. Hindry and J. H. Silverman, Diophantine geometry. An introduction, Graduate Texts in Mathematics 201. Springer-Verlag, New York, 2000. xiv+558 pp
• \au{E. Hrushovski} \ti{The Mordell-Lang conjecture for function fields} \jo{J. Amer. Math. Soc.} \vo{9} \yr{1996} \pps{667–690}
• —, \ti{Proof of Manin’s theorem by reduction to positive characteristic} \pps{197–205} Model Theory and Algebraic Geometry, Lecture Notes in Mathematics 1696, Elisabeth Bouscaren (Ed.), 1999.
• B. Hutz, Good reduction of periodic points on projective varieties, Illinois J. Math. 53 (2009), 1109–1126.
• S. Iitaka, Logarithmic forms of algebraic varieties, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), no. 3, 525–544.
• P. Ingram and J. H. Silverman, Primitive divisors in arithmetic dynamics, Math. Proc. Cambridge Philos. Soc. 146 (2009), 289–302.
• J. Jost, Riemannian geometry and geometric analysis, third ed., Universitext, Springer-Verlag, Berlin, 2002.
• S. Kawaguchi and J. H. Silverman, Examples of dynamical degree equals arithmetic degree, Michigan Math. J. 63 (2014), no. 1, 41–63.
• \au{D. S. Keeler, D. Rogalski, and J.T. Stafford} \ti{Naïve noncommutative blowing up} \jo{Duke Math. J.} \vo{126} \yr{2005} \pps{491–546}
• R. Jones, The density of prime divisors in the arithmetic dynamics of quadratic polynomials, J. Lond. Math. Soc. (2) 78 (2008), no. 2, 523–544.
• R. Jones, Galois representations from pre-image trees: an arboreal survey, Pub. Math. Besançon. (2013), 107–136
• —, Fixed-point-free elements of iterated monodromy groups, Trans. Amer. Math. Soc., 367(3):2023-2049, 2015.
• R. Jones, J. Cahn, and J. Spear, Powers in orbits of rational functions: cases of an arithmetic dynamical Mordell-Lang conjecture, in preparation.
• J. Juul, P. Kurlberg, K. Madhu, and T. J. Tucker, Wreath products and proportions of periodic points, to appear in Int. Math. Res. Not. IMRN.
• \au{S. Lang} \ti{Integral points on curves} \jo{Publ. Math. IHES} \vo{6} \yr{1960} \pps{27–43}
• —, \ti{Fundamentals of Diophantine geometry} Springer-Verlag, New York, 1983.
• —, Algebra, third ed., Springer-Verlag, New York, 2002, xvi+914 pp.
• M. Laurent, Equations diophantiennes exponentielles, Invent. Math. 78 (1984), 299–327.
• \au{C. Lech} \ti{A note on recurring series} \jo{Ark. Mat.} \vo{2} \yr{1953} \pps{417–421}
• A. Levin, The exceptional set in Vojta’s conjecture for algebraic points of bounded degree, Proc. Amer. Math. Soc. 140 (2012), no. 7, 2267–2277.
• A. Levin and Y. Yasufuku Integral points and orbits of endomorphisms on the projective plane, preprint.
• \au{K. Mahler} \ti{Eine arithmetische Eigenshaft der Taylor-Koeffizienten rationaler Funktionen} \jo{Proc. Kon. Ned. Akad. Wetensch.} \vo{38} \yr{1935} \pps{50–60}
• —, An interpolation series for continuous functions of a $p$-adic variable, J. Reine Angew. Math. 199 (1958), 23–34.
• —, A correction to the paper “an interpolation series for continuous functions of a $p$-adic variable”, J. Reine Angew. Math. 208 (1961), 70–72.
• \au{D. Masser and U. Zannier} \ti{Torsion anomalous points and families of elliptic curves} \jo{C. R. Math. Acad. Sci. Paris} \vo{346} \yr{2008} \pps{491–494}
• —\ti{Torsion anomalous points and families of elliptic curves} \jo{Amer. J. Math.} \vo{132} \yr{2010} \pps{1677–1691}
• —\ti{Torsion points on families of squares of elliptic curves} Math. Ann. 352 (2012), 453–484.
• H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986, Translated from the Japanese by M. Reid.
• A. Medvedev, Minimal sets in $ACFA$, PhD thesis, UC Berkeley, 2007.
• A. Medvedev and T. Scanlon, Invariant varieties for polynomial dynamical systems, Ann. Math. (2) 179 (2014), no. 1, 81–177.
• \au{C. Methfessel} \ti{On the zeros of recurrence sequences with non-constant coefficients} \jo{Arch. Math. (Basel)} \vo{74} \yr{2000} \pps{201–206}
• \au{R. Moosa and T. Scanlon} \ti{The Mordell-Lang Conjecture in positive characteristic revisited} Model Theory and Applications (eds. L. Bélair, P. D’Aquino, D. Marker, M. Otero, F. Point, & A. Wilkie), 2003, 273–296.
• —\ti{$F$-structures and integral points on semiabelian varieties over finite fields} \jo{Amer. J. Math.} \vo{126} \yr{2004} \pps{473–522}
• P. Morton and J. H. Silverman, Rational periodic points of rational functions, Internat. Math. Res. Notices (1994), no. 2, 97–110.
• —, Periodic points, multiplicities, and dynamical units, J. Reine Angew. Math. 461 (1995), 81–122.
• D. Mumford, A remark on Mordell’s conjecture, Amer. J. Math. 87 (1965), 1007–1016.
• \au{P. Müller and M. E. Zieve} \ti{On Ritt’s polynomial decomposition theorems} submitted for publication.
• V. Nekrashevych, Self-similar groups, volume 117 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2005.
• T. W. Ng and M.-X. Wang, Ritt’s theory on the unit disk, Forum Math. 25 (2013), 821–851.
• K. Nguyen, Some arithmetic dynamics of diagonally split polynomial maps, Int. Math. Res. Not. IMRN, vol. 2015, 1159–1199.
• \au{K. Nguyen and M. E. Zieve} \ti{Algebraic dynamics of split morphisms associated to rational maps having generic ramification} preprint.
• —\ti{Functional equations and the curves $f(X)=g(Y)$ for generic $f$ and arbitrary $g$} preprint.
• R. W. K. Odoni, The Galois theory of iterates and composites of polynomials, Proc. London Math. Soc. (3) 51 (1985), no. 3, 385–414.
• \au{A. Ostafe and M. Sha} \ti{On the quantitative Dynamical Mordell-Lang Conjecture} preprint.
• \au{F. Pazuki} \ti{Zhang’s conjecture and squares of abelian surfaces} \jo{C. R. Math. Acad. Sci. Paris} \yr{2010} \vo{348} \pps{483–486}
• T. Pezda, Cycles of polynomial mappings in several variables over rings of integers in finite extensions of the rationals. II, Monatsh. Math. 145 (2005), no. 4, 321–331.
• C. Petsche, On the distribution of orbits in affine varieties, preprint, \xxx11401.3425.
• J. Pila and U. Zannier, Rational points in periodic analytic sets and the Manin- Mumford conjecture, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19 (2008), 149–162.
• A. Pillay, The model-theoretic content of Lang’s conjecture, Model Theory and Algebraic Geometry, Lecture Notes in Math. 1696 (E. Bouscaren, ed.), Springer-Verlag, Berlin, 1998, pp. 101–106.
• J. Piñeiro, L. Szpiro, and T. Tucker, Mahler measure for dynamical systems on $\mathbb {P}^{1}$ and intersection theory on a singular arithmetic surface, Geometric methods in algebra and number theory (F. Bogomolov and Y. Tschinkel, eds.), Progress in Mathematics 235, Birkhäuser, 2004, pp. 219–250.
• \au{R. Pink} \ti{A common generalization of the conjectures of André-Oort, Manin-Mumford, and Mordell-Lang} unpublished manuscript, 2005.
• J. M. Pollard, A Monte Carlo method for factorization, Nordisk Tidskr. Informationsbehandling (BIT) 15 (1975), no. 3, 331–334.
• B. Poonen, Local height functions and the Mordell-Weil theorem for Drinfeld modules, Compositio Math. 97 (1995), 349–368.
• —, $p$-adic interpolation of iterates, Bull. London Math. Soc. 46 (2014), no. 3, 525–527.
• B. Poonen and J. F. Voloch, The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields. Ann. Math. 171 (2010), 511–532.
• M. Raynaud, Courbes sur une variété abélienne et points de torsion, Invent. Math. 71 (1983), 207–233.
• —, Sous-variétés d’une variété abélienne et points de torsion, Arithmetic and geometry, vol. I, Progr. Math., vol. 35, Birkhäuser, Boston, MA, 1983, pp. 327–352.
• \au{J. F. Ritt} \ti{On the iteration of rational functions} \jo{Trans. Amer. Math. Soc.} \vo{21} \yr{1920} \pps{348–356}
• J. Rivera-Letelier, Dynamique des fonctions rationnelles sur des corps locaux, Astérisque (2003), no. 287, 147–230, Geometric methods in dynamics. II.
• A. M. Robert, A course in $p$-adic analysis, Graduate Texts in Mathematics, vol. 198, Springer-Verlag, New York, 2000.
• L. A. Rubel, Some research problems about algebraic differential equations, Trans. Amer. Math. Soc. 280 (1983), 43–52.
• T. Scanlon, Diophantine geometry of the torsion of a Drinfeld module, J. Number Theory 97 (2002), no. 1, 10–25.
• —, A Euclidean Skolem-Mahler-Lech-Chabauty method, Math. Res. Lett. 18 (2011), 835–842.
• —, Analytic relations on a dynamical orbit, preprint.
• \au{T. Scanlon and Y. Yasufuku} \ti{Exponential-polynomial equations and dynamical return sets} \jo{Int. Math. Res. Not. IMRN} 2014, no. 16, 4357–4367.
• I. R. Shafarevich, Basic algebraic geometry, study ed., Springer-Verlag, Berlin, 1977, Translated from the Russian by K. A. Hirsch, Revised printing of Grundlehren der mathematischen Wissenschaften, Vol. 213, 1974.
• A. Schinzel, Primitive divisors of the expression $a^n-b^n$ in algebraic number fields, J. Reine Angew. Math. 268/269 (1974), 27–33.
• \au{W. M. Schmidt} \ti{The zero multiplicity of linear recurrence sequences} \jo{Acta Math.} \vo{182} \yr{1999} \pps{243–282}
• —\ti{Zeros of linear recurrence sequences} \jo{Publ. Math. Debrecen} \vo{56} \yr{2000} \pps{609–630}
• \au{H. Sharif and C. F. Woodcock} \ti{Algebraic functions over a field of positive characteristic and Hadamard products} \jo{J. London Math. Soc. (2)} \vo{37} \yr{1988} \pps{no. 3, 395–403}
• \au{C. L. Siegel} \ti{Über einige Anwendungen Diophantischer Approximationen} \jo{Abh. Preuss. Akad. Wiss. Phys. Math. Kl.} \yr{1929} \pps{41–69} (Reprinted as pp. 209–266 of his Gesammelte Abhandlungen I, Springer, Berlin, 1966.)
• \au{J. H. Silverman} \ti{Heights and the specialization map for families of abelian varieties} \jo{J. Reine Angew. Math.} \vo{342} \yr{1983} \pps{197–211}
• —, \ti{Integer points, Diophantine approximation, and iteration of rational maps} \jo{Duke Math. J.} \vo{71} \yr{1993} \pps{793–829}
• —, The arithmetic of dynamical systems, Graduate Texts in Mathematics 241, Springer, New York, 2007, x+511 pp.
• —, Variation of periods modulo p in arithmetic dynamics, New York J. Math. 14 (2008), 601–616.
• —, Primitive divisors, dynamical Zsigmondy sets, and Vojta’s conjecture, J. Number Theory 133 (2013), no. 9, 2948–2963.
• J. H. Silverman and B. Viray, On a uniform bound for the number of exceptional linear subvarieties in the Mordell-Lang conjecture, Math. Res. Lett. 20 (2013), no. 3, 547–566.
• J. H. Silverman and J. F. Voloch, A Local-Global Criterion for Dynamics on $\bP ^1$, Acta Arith. 137 (2009), 285–294.
• \au{T. Skolem} \ti{Ein Verfahren zur Behandlung gewisser exponentialer Gleichungen und diophantischer Gleichungen} Comptes Rendus Congr. Math. Scand. (Stockholm, 1934) 163–188.
• \au{V. Sookdeo} \ti{Integer points in backward orbits} J. Number Theory 131 (2011), 1229–1239.
• \au{V. Srinivas} \ti{On the embedding dimension of an affine variety} \jo{Math. Ann.} \yr{1991} \vo{289} \pps{125–132}
• \au{P. Stevenhagen and H. W. Lenstra Jr.} \ti{Chebotarev and his density theorem} \jo{Math. Intelligencer} \vo{18} \yr{1996} \pps{26–37}
• M. Stoll, Galois groups over $\textbf {Q}$ of some iterated polynomials, Arch. Math. (Basel) 59 (1992), no. 3, 239–244.
• C.-L. Sun, Adélic points of subvarieties of isotrivial semi-abelian varieties over a global field of positive characteristic, preprint, \xxx1005.4998
• \au{E. Szemerédi} \ti{On sets of integers containing no $k$ elements in arithmetic progression} \jo{Acta Arithm.} \vo{27} \yr{1975} \pps{199–245}
• L. Szpiro, E. Ullmo, and S. Zhang, Équirépartition des petits points (French) [Uniform distribution of small points], Invent. Math. 127 (1997), 337–347.
• E. Ullmo, Positivité et discrétion des points algébriques des courbes, Ann. of Math. (2) 147 (1998), 167–179.
• T. J. Tucker, Integer points in arithmetic sequences, Bull. Inst. Math. Acad. Sin. (N.S.) 9 (2014), no. 4, 633–639.
• P. Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987.
• —\ti{Mordell’s conjecture over function fields} \jo{Invent. Math.} \vo{98} \yr{1989} \pps{115–138}
• —\ti{Integral points on subvarieties of semiabelian varieties. I} \jo{Invent. Math.} \vo{126} \yr{1996} \pps{133–181}
• —, Integral points on subvarieties of semiabelian varieties. II, Amer. J. Math. 121 (1999), no. 2, 283–313.
• M. Wang, Endomorphisms of uniformization spaces, preprint.
• A. J. Wilkie, Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function J. Amer. Math. Soc. 9 (1996), 1051–1094.
• J. Xie, Dynamical Mordell-Lang Conjecture for birational polynomial morphisms on $\bA ^2$, Math. Ann. 360 (2014), no. 1-2, 457–480.
• —, Intersection of valuation rings in $k[x,y]$, preprint available on \xxx{1403.6052}
• —, The Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane, preprint available on \xxx{1503.00773}
• Y Yasufuku, Vojta’s conjecture and dynamics, Algebraic number theory and related topics 2009, RIMS Kôkyûroku Bessatsu, B25, Res. Inst. Math. Sci. (RIMS), Kyoto, 2011, pp. 75–86.
• —, Deviations from $S$-integrality in orbits on $\mathbb {P}^N$, Bull. Inst. Math. Acad. Sin. (N.S.) 9 (2014), no. 4, 603–631.
• —, Integral points and relative sizes of coordinates of orbits in $\mathbb {P}^N$, Math. Z. 279 (2015), no. 3-4, 1121–1141.
• K. Yu, Linear forms in $p$-adic logarithms. II, Compositio Math. 74 (1990), 15–113.
• X. Yuan, Big line bundles over arithmetic varieties, Invent. Math. 173 (2008), 603–649.
• X. Yuan and S.-W. Zhang, Calabi theorem and algebraic dynamics, preprint, 23 pages.
• U. Zannier, Lecture notes on Diophantine analysis, Appunti. Scuola Normale Superiore di Pisa (Nuova Serie) [Lecture Notes. Scuola Normale Superiore di Pisa (New Series)], vol. 8, Edizioni della Normale, Pisa, 2009, With an appendix by Francesco Amoroso.
• —, Some problems of unlikely intersections in arithmetic and geometry, Annals of Mathematics Studies, vol. 181, Princeton University Press, Princeton, NJ, 2012, With appendixes by David Masser.
• S. Zhang, Small points and adelic metrics, J. Algebraic Geometry 4 (1995), 281–300.
• —, Equidistribution of small points on abelian varieties, Ann. of Math. (2) 147 (1998), 159–165.
• —, Distributions in algebraic dynamics, Survey in Differential Geometry, vol. 10, International Press, 2006, pp. 381–430.
• M. E. Zieve, Cycles of polynomial mappings, PhD thesis, University of California at Berkeley, 1996
• —, Decompositions of Laurent polynomials, preprint.
• K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math. Phys. 3 (1892) 265–284.