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Bibliography for Arithmetic Dynamical Systems Bibliography for Arithmetic Dynamics Joseph H. Silverman May 5, 2020 This document lists a wide variety of articles and books in the area of arithmetic dynamics. It also includes some additional material that was referenced in The Arith- metic of Dynamical Systems (Springer-Verlag GTM 241) and some miscellaneous ar- ticles and books that I’ve referenced in my own work. Note that the numbering in this document does not match the numbering of references in GTM 241. Further note that I do not automatically update ArXiv preprints when they appear. Most recent pub- lished articles in arithmetic dynamics can be found by searching the 37P category on MathSciNet. References [1] N. Abarenkova, J.-C. Angles` d’Auriac, S. Boukraa, S. Hassani, and J.-M. Maillard. Topological entropy and Arnold complexity for two-dimensional mappings. Phys. Lett. A, 262(1):44–49, 1999. [2] W. Abram and J. C. Lagarias. Intersections of multiplicative translates of 3-adic cantor sets, 2013. arXiv:1308.3133. [3] R. L. Adler, A. G. Konheim, and M. H. McAndrew. Topological entropy. Trans. Amer. Math. Soc., 114:309–319, 1965. [4] L. V. Ahlfors. Complex Analysis. McGraw-Hill Book Co., New York, 1978. [5] F. Ahmad, R. L. Benedetto, J. Cain, G. Carroll, and L. Fang. The arithmetic basilica: a quadratic PCF arboreal Galois group, 2019. arXiv:1909.00039. [6] O. Ahmadi. A note on stable quadratic polynomials over fields of characteristic two, 2009. arXiv:0910.4556. [7] O. Ahmadi, F. Luca, A. Ostafe, and I. E. Shparlinski. On stable quadratic polynomials. Glasg. Math. J., 54(2):359–369, 2012. [8] O. Ahmadi and K. Monsef-Shokri. A note on the stability of trinomials over finite fields, 2018. arXiv:1810.03142. [9] A. V. Aho and N. J. A. Sloane. Some doubly exponential sequences. Fibonacci Quart., 11(4):429–437, 1973. [10] N. Ailon and Z. Rudnick. Torsion points on curves and common divisors of ak − 1 and bk − 1. Acta Arith., 113(1):31–38, 2004. [11] W. Aitken, F. Hajir, and C. Maire. Finitely ramified iterated extensions. IMRN, 14:855– 880, 2005. [12] A. Akbary and D. Ghioca. Periods of orbits modulo primes. J. Number Theory, 129(11):2831–2842, 2009. [13] S. Akiyama, H. Brunotte, A. Petho,˝ and W. Steiner. Periodicity of certain piecewise affine planar maps. Tsukuba J. Math., 32(1):197–251, 2008. 1 [14] S. Albeverio, M. Gundlach, A. Khrennikov, and K.-O. Lindahl. On the Markovian behavior of p-adic random dynamical systems. Russ. J. Math. Phys., 8(2):135–152, 2001. [15] S. Albeverio, U. A. Rozikov, and I. A. Sattarov. p-adic (2; 1)-rational dynamical sys- tems. J. Math. Anal. Appl., 398(2):553–566, 2013. [16] S. Albeverio, B. Tirotstsi, A. Y. Khrennikov, and S. de Shmedt. p-adic dynamical sys- tems. Teoret. Mat. Fiz., 114(3):349–365, 1998. [17] N. Ali. Stabilite´ des polynomes.ˆ Acta Arith., 119(1):53–63, 2005. [18] I. Aliev and C. Smyth. Power maps and subvarieties of the complex algebraic n-torus, 2008. arXiv:0802.2938. [19] K. Allen, D. DeMark, and C. Petsche. Non-Archimedean Henon´ maps, attractors, and horseshoes. Res. Number Theory, 4(1):Art. 5, 30, 2018. [20] E. Amerik. A computation of invariants of a rational self-map. Ann. Fac. Sci. Toulouse Math. (6), 18(3):445–457, 2009. [21] E. Amerik. Existence of non-preperiodic algebraic points for a rational self-map of infinite order. Math. Res. Lett., 18(2):251–256, 2011. [22] E. Amerik. Some applications of p-adic uniformization to algebraic dynamics. In Ra- tional points, rational curves, and entire holomorphic curves on projective varieties, volume 654 of Contemp. Math., pages 3–21. Amer. Math. Soc., Providence, RI, 2015. [23] E. Amerik, F. Bogomolov, and M. Rovinsky. Remarks on endomorphisms and rational points. Compos. Math., 147(6):1819–1842, 2011. [24] E. Amerik, P. Kurlberg, K. D. Nguyen, A. Towsley, B. Viray, and J. F. Voloch. Evidence for the dynamical Brauer-Manin criterion. Exp. Math., 25(1):54–65, 2016. [25] E. Amerik and M. Verbitsky. Construction of automorphisms of hyperkahler¨ manifolds. Compos. Math., 153(8):1610–1621, 2017. [26] F. Amoroso and R. Dvornicich. A lower bound for the height in abelian extensions. J. Number Theory, 80(2):260–272, 2000. [27] F. Amoroso and U. Zannier. A relative Dobrowolski lower bound over abelian exten- sions. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 29(3):711–727, 2000. [28] V. Anashin. Ergodic transformations in the space of p-adic integers. In p-adic math- ematical physics, volume 826 of AIP Conf. Proc., pages 3–24. Amer. Inst. Phys., Melville, NY, 2006. [29] J. Anderson. Bounds on the radius of the p-adic Mandelbrot set. Acta Arith., 158(3):253–269, 2013. [30] J. Anderson, I. Bouw, O. Ejder, N. Girgin, V. Karemaker, and M. Manes. Dynamical belyi maps, 2017. arXiv:1703.08563. [31] J. Anderson, S. Hamblen, B. Poonen, and L. Walton. Local arboreal representations. Int. Math. Res. Not. IMRN, (19):5974–5994, 2018. [32] J. Anderson, M. Manes, and B. Tobin. Cubic post-critically finite polynomials defined over Q, 2020. arXiv:2001.10471. [33] Y. Andre.´ G-functions and geometry. Aspects of Mathematics, E13. Friedr. Vieweg & Sohn, Braunschweig, 1989. [34] K. Andrei and E. Yurova. Criteria of ergodicity for p-adic dynamical systems in terms of coordinate functions, 2013. arXiv:1303.6472. [35] J. Andrews and C. Petsche. Abelian extensions in dynamical Galois theory, 2020. arXiv:2001.00659. [36] J.-C. Angles` d’Auriac, J.-M. Maillard, and C. M. Viallet. On the complexity of some birational transformations. J. Phys. A, 39(14):3641–3654, 2006. [37] O. Antol´ın-Camarena and S. Koch. On a theorem of Kas and Schlessinger. In Quasicon- formal mappings, Riemann surfaces, and Teichmuller¨ spaces, volume 575 of Contemp. Math., pages 13–22. Amer. Math. Soc., Providence, RI, 2012. 2 [38] T. M. Apostol. Introduction to Analytic Number Theory. Springer-Verlag, New York, 1976. Undergraduate Texts in Mathematics. [39] M. Arfeux. Approximability of dynamical systems between trees of spheres. Indiana Univ. Math. J., 65(6):1945–1977, 2016. [40] M. Arfeux. Compactification and trees of spheres covers. Conform. Geom. Dyn., 21:225–246, 2017. [41] M. Arfeux. Dynamics on trees of spheres. J. Lond. Math. Soc. (2), 95(1):177–202, 2017. [42] M. Arfeux and J. Kiwi. Irreducibility of the set of cubic polynomials with one periodic critical point, 2016. arXiv:1611.09281. [43] J. Arias de Reyna. Dynamical zeta functions and Kummer congruences. Acta Arith., 119(1):39–52, 2005. [44] V. I. Arnol0d. Dynamics of complexity of intersections. Bol. Soc. Brasil. Mat. (N.S.), 21(1):1–10, 1990. [45] V. I. Arnol0d. Dynamics of intersections. In Analysis, et cetera, pages 77–84. Academic Press, Boston, MA, 1990. [46] V. I. Arnol0d. Dynamics, statistics and projective geometry of Galois fields. Cambridge University Press, Cambridge, 2011. Translated from the Russian, With words about Arnold by Maxim Kazarian and Ricardo Uribe-Vargas. [47] D. K. Arrowsmith and F. Vivaldi. Some p-adic representations of the Smale horseshoe. Phys. Lett. A, 176(5):292–294, 1993. [48] D. K. Arrowsmith and F. Vivaldi. Geometry of p-adic Siegel discs. Phys. D, 71(1- 2):222–236, 1994. [49] M. Astorg. Dynamics of post-critically finite maps in higher dimension. Ergodic Theory Dynam. Systems, 2018. DOI: https://doi.org/10.1017/etds.2018.32. [50] P. Autissier. Hauteur des correspondances de Hecke. Bull. Soc. Math. France, 131(3):421–433, 2003. [51] P. Autissier. Dynamique des correspondances algebriques´ et hauteurs. Int. Math. Res. Not., (69):3723–3739, 2004. [52] S. Axler. Linear Algebra Done Right. Undergraduate Texts in Mathematics. Springer- Verlag, New York, second edition, 1997. [53] M. Ayad. Periodicit´ e´ (mod q) des suites elliptiques et points S-entiers sur les courbes elliptiques. Ann. Inst. Fourier (Grenoble), 43(3):585–618, 1993. [54] M. Ayad and D. L. McQuillan. Irreducibility of the iterates of a quadratic polynomial over a field. Acta Arith., 93(1):87–97, 2000. [55] M. Ayad and D. L. McQuillan. Corrections to: “Irreducibility of the iterates of a quadratic polynomial over a field” [Acta Arith. 93 (2000), no. 1, 87–97]. Acta Arith., 99(1):97, 2001. [56] A. Azevedo, M. Carvalho, and A. Machiavelo. Dynamics of a quasi-quadratic map, 2012. arXiv:1210.0042. [57] E. Bach and A. Bridy. On the number of distinct functional graphs of affine-linear transformations over finite fields. Linear Algebra Appl., 439(5):1312–1320, 2013. [58] G. Baier and M. Klein. Maximum hyperchaos in generalized Henon´ maps. Physics Letters A, 151:281–284, 12 1990. [59] S. Baier, S. Jaidee, S. Stevens, and T. Ward. Automorphisms with exotic orbit growth, 2012. arXiv:1201.4503. [60] D. Bajpai, R. Benedetto, R. Chen, E. Kim, O. Marschall, D. Onul, and Y. Xiao. Non- archimedean connected Julia sets with branching, 2014. arXiv:1410.0591. [61] A. Baker. Transcendental number theory. Cambridge Mathematical Library. Cambridge University Press, Cambridge, second edition, 1990. 3 [62] I. N. Baker. Fixpoints of polynomials and rational functions. J. London Math. Soc., 39:615–622, 1964. [63] M. Baker. A lower bound for average values of dynamical Green’s functions. Math. Res. Lett., 13(2-3):245–257, 2006. [64] M. Baker. Uniform structures and Berkovich spaces, 2006. ArXiv:math.NT/ 0606252. [65] M. Baker. A finiteness theorem for canonical heights attached to rational maps over function fields. J. Reine Angew. Math., 626:205–233, 2009. [66] M. Baker and L. De Marco. Special curves and postcritically finite polynomials. Forum Math. Pi, 1:e3, 35, 2013. [67] M. Baker and L.
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