Current Trends and Open Problems in Arithmetic Dynamics

TL;DR

This paper surveys recent progress and open problems in arithmetic dynamics, a field studying number theoretic properties of dynamical systems inspired by classical arithmetic geometry and complex dynamics.

Contribution

It provides an overview of key problems and recent developments in the emerging field of arithmetic dynamics.

Findings

Identification of key open problems in the field

Summary of recent advances in number theoretic properties of dynamical systems

Highlighting interdisciplinary connections with arithmetic geometry and complex dynamics

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.