Arithmetic Problems in Dynamical Systems

In discrete dynamical systems, the ultimate goal is to understand the asymptotic behavior of all points under iterated compositions of a certain transformation (self-map) of a certain space. In arithmetic dynamics, the asymptotic behavior of points with coordinates of arithmetic interest (algebraic numbers or p-adic numbers) is examined. In connection with arithmetic dynamics, some problems are reduced to the determination of rational points on curves. This article introduces the issues in arithmetic dynamics related to these problems. © 2024 Nippon Telegraph and Telephone Corp.. All rights reserved.