用户: Lieriheart/算术动力系统与相交问题/参考文献

[ACZ] Y. André, P. Corvaja, and U. Zannier. The Betti map associated to a section of an abelian scheme. Invent. Math. 222(2020), 161-202.

[Ba] Matthew Baker. A finiteness theorem for canonical heights attached to rational maps over function fields. J. Reine Angew. Math. 626(2009), 205-233.

[BR] Matthew Baker and Robert Rumely. Potential theory and dynamics on the Berkovich projective line, volume 159 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2010.

[BB] Giovanni Bassanelli and François Berteloot. Bifurcation currents in holomorphic dynamics on . J. Reine Angew. Math. 608(2007), 201-235.

[BT] Eric Bedford and B.A. Taylor. A new capacity for plurisubharmonic functions. Acta Math. .

[BB] François Berteloot and Fabrizio Bianchi. Stability and bifurcations in projective holomorphic dynamics. In Dynamical systems, volume 115 of Banach Center Publ., pages 37-71. Polish Acad. Sci. Inst. Math., Warsaw, 2018.

[BBD] François Berteloot, Fabrizio Bianchi, and Christophe Dupont. Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of . Ann. Sci. Éc. Norm. Supér. (4) .

[BFT] Fedor Bogomolov, Hang Fu, and Yuri Tschinkel. Torsion of elliptic curves and unlikely intersections. In Geometry and physics. Vol. I, pages 19-37. Oxford Univ. Press, Oxford, 2018.

[BT] Fedor Bogomolov and Yuri Tschinkel. Algebraic varieties over small fields. In Diophantine geometry, volume 4 of CRM Series, pages 73-91. Ed. Norm., Pisa, 2007.

[Br] Hans Brolin. Invariant sets under iteration of rational functions. Ark. Mat. 6(1965), 103144.

[CS] Gregory S. Call and Joseph H. Silverman. Canonical heights on varieties with morphisms. Compositio Math. 89(1993), 163-205.

[CGHX] Serge Cantat, Ziyang Gao, Philipp Habegger, and Junyi Xie. The geometric Bogomolov conjecture. Duke Math. J. 170(2021), 247-277.

[CH1] Zoé Chatzidakis and Ehud Hrushovski. Difference fields and descent in algebraic dynamics. I. J. Inst. Math. Jussieu .

[CDMZ] Pietro Corvaja, Julian Demeio, David Masser, and Umberto Zannier. On the torsion values for sections of an elliptic scheme. Preprint, arXiv:1909.01253v2 [math.AG] .

[Dem] Jean-Pierre Demailly. Complex Analytic and Differential Geometry. Version of June 21, 2012.

[De1] Laura DeMarco. Dynamics of rational maps: a current on the bifurcation locus. Math. Res. Lett. 8(2001), 57-66.

[De2] Laura DeMarco. Bifurcations, intersections, and heights. Algebra Number Theory. . [De3] Laura DeMarco. Dynamical moduli spaces and elliptic curves (KAWA Lecture Notes). Ann. Fac. Sci. Toulouse Math. 27(2018), 389-420.

[DKY] Laura DeMarco, Holly Krieger, and Hexi Ye. Uniform Manin-Mumford for a family of genus 2 curves. Ann. of Math. (2) 191(2020), 949-1001.

[DM] Laura DeMarco and Niki Myrto Mavraki. Dynamics on  : preperiodic points and pairwise stability. Preprint, arXiv:2212.13215v2 [math.DS].

[DGH1] Vesselin Dimitrov, Ziyang Gao, and Philipp Habegger. Uniformity in Mordell-Lang for curves. Ann. of Math. (2) 194(2021), 237-298.

[DGH2] Vesselin Dimitrov, Ziyang Gao, and Philipp Habegger. A consequence of the relative Bogomolov conjecture. J. Number Theory , 146-160.

[DS] Tien-Cuong Dinh and Nessim Sibony. Introduction to the theory of currents. Lecture notes 2005, https://webusers.imj-prg.fr/ tien-cuong.dinh/Cours2005/Master/cours.pdf.

[DH] A. Douady and J. H. Hubbard. A proof of Thurston’s topological characterization of rational functions. Acta Math. 171(1993), 263-297.

Romain Dujardin and Charles Favre. Distribution of rational maps with a preperiodic critical point. Amer. J. Math. 130(2008), 979-1032.

[Dup] Christophe Dupont. Exemples de Lattès et domaines faiblement sphériques de . Manuscripta Math. 111(2003), 357-378.

[Fa] Najmuddin Fakhruddin. Questions on self maps of algebraic varieties. J. Ramanujan Math. Soc. 18(2003), 109-122.

[FS1] John Erik Fornæss and Nessim Sibony. Complex dynamics in higher dimension. I. Astérisque (1994), 5, 201-231. Complex analytic methods in dynamical systems (Rio de Janeiro, 1992).

[FS] John Erik Fornæss and Nessim Sibony. Complex dynamics in higher dimensions. In Complex Potential Theory (Montreal, PQ, 1993), pages 131-186. Kluwer Acad. Publ., Dordrecht, 1994.

[FS2] John Erik Fornæss and Nessim Sibony. Complex dynamics in higher dimension. II. In Modern Methods in Complex Analysis (Princeton, NJ, 1992), pages 135-182. Princeton Univ. Press, Princeton, NJ, 1995.

[FLM] Alexandre Freire, Artur Lopes, and Ricardo Mañé. An invariant measure for rational maps. Bol. Soc. Brasil. Mat. 14(1983), 45-62.

[GGK] Ziyang Gao, Tangli Ge, and Lars Kühne. The Uniform Mordell-Lang Conjecture. Preprint, arXiv:2105.15085v2 [math.NT].

[Ga] Thomas Gauthier. Good height functions on quasiprojective varieties: equidistribution and applications in dynamics. Preprint, arXiv:2105.02479v3 [math.NT].

[GV] Thomas Gauthier and Gabriel Vigny. The geometric dynamical Northcott and Bogomolov properties. Preprint, arXiv:1912.07907v2 [math.DS].

[Kl] Maciej Klimek. Pluripotential Theory. The Clarendon Press Oxford University Press, New York, 1991. Oxford Science Publications.

[Kü1] Lars Kühne. Equidistribution in families of abelian varieties and uniformity. Preprint, arXiv:2101.10272v3 [math.NT].

[Kü2] Lars Kühne. The Relative Bogomolov Conjecture for Fibered Products of Elliptic Surfaces. Preprint, arXiv:2103.06203 [math.NT].

[LN] S. Lang and A. Néron. Rational points of abelian varieties over function fields. Amer. J. Math. 81(1959), 95-118. [LP] G. Levin and F. Przytycki. When do two rational functions have the same Julia set? Proc. Amer. Math. Soc. 125(1997), 2179-2190.

[Ly1] M. Lyubich. Entropy properties of rational endomorphisms of the Riemann sphere. Ergodic Theory Dynamical Systems 3(1983), 351-385.

[Ly2] M. Yu. Lyubich. Some typical properties of the dynamics of rational mappings. Uspekhi Mat. Nauk 38(1983), 197-198.

[MSS] R. Mañé, P. Sad, and D. Sullivan. On the dynamics of rational maps. Ann. Sci. Ec. Norm. Sup. 16(1983), 193-217.

[MS] Niki Myrto Mavraki and Harry Schmidt. On the dynamical Bogomolov conjecture for families of split rational maps. Preprint, arXiv:2201.10455v3 [math.NT].

[Mc1] Curtis T. McMullen. Families of rational maps and iterative root-finding algorithms. Ann. of Math. (2) 125(1987), 467-493.

[Mc2] Curtis T. McMullen. Complex Dynamics and Renormalization. Princeton University Press, Princeton, NJ, 1994.

[McS] Curtis T. McMullen and Dennis P. Sullivan. Quasiconformal homeomorphisms and dynamics. III. The Teichmüller space of a holomorphic dynamical system. Adv. Math. 135(1998), .

[Mi1] John Milnor. Dynamics in One Complex Variable, volume 160 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, Third edition, 2006.

[Mi2] John Milnor. On Lattès maps. In Dynamics on the Riemann sphere, pages 9-43. Eur. Math. Soc., Zürich, 2006.

[MS] Patrick Morton and Joseph H. Silverman. Rational periodic points of rational functions. Internat. Math. Res. Notices (1994), .

[Po] Jerome Poineau. Dynamique analytique sur II : Écart uniforme entre Lattès et conjecture de Bogomolov-Fu-Tschinkel. Preprint, arXiv:2207.01574 [math.NT].

[Ra1] Thomas Ransford. Potential Theory in the Complex Plane. Cambridge University Press, Cambridge, 1995.

[Ra2] M. Raynaud. Courbes sur une variété abélienne et points de torsion. Invent. Math. .

[Si1] Joseph H. Silverman. The Arithmetic of Dynamical Systems, volume 241 of Graduate Texts in Mathematics. Springer, New York, 2007.

[Si2] Joseph H. Silverman. The Arithmetic of Elliptic Curves, volume 106 of Graduate Texts in Mathematics. Springer, Dordrecht, second edition, 2009.

[Si3] Joseph H. Silverman. Moduli spaces and arithmetic dynamics, volume 30 of CRM Monograph Series. American Mathematical Society, Providence, RI, 2012.

[SUZ] L. Szpiro, E. Ullmo, and S. Zhang. Équirépartition des petits points. Invent. Math. .

[UU1] Douglas Ulmer and Giancarlo Urzúa. Bounding tangencies of sections on elliptic surfaces. Int. Math. Res. Not. IMRN (2021), 4768-4802.

[UU2] Douglas Ulmer and Giancarlo Urzúa. Transversality of sections on elliptic surfaces with applications to elliptic divisibility sequences and geography of surfaces. Selecta Math. (N.S.) 28(2022), Paper No. 25, 36 .

[YZ] Xinyi Yuan and Shouwu Zhang. Adelic line bundles over quasiprojective varieties. Preprint, arXiv:2105.13587v4