Current trends and open problems in arithmetic dynamics

Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph; Tucker, Thomas

doi:10.1090/bull/1665

Current trends and open problems in arithmetic dynamics
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by Robert Benedetto, Patrick Ingram, Rafe Jones, Michelle Manes, Joseph H. Silverman and Thomas J. Tucker PDF

Bull. Amer. Math. Soc. 56 (2019), 611-685 Request permission

Abstract:

Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry and partly from $p$-adic analogues of theorems and conjectures in classical complex dynamics. In this article we survey some of the motivating problems and some of the recent progress in the field of arithmetic dynamics.

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