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Current trends and open problems in arithmetic dynamics. (English) Zbl 07124524
Summary: 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.

MSC:
37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps
37P15 Dynamical systems over global ground fields
37P20 Dynamical systems over non-Archimedean local ground fields
37P25 Dynamical systems over finite ground fields
37P30 Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems
37P45 Families and moduli spaces in arithmetic and non-Archimedean dynamical systems
37P55 Arithmetic dynamics on general algebraic varieties
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