nLab algebraic dynamics

While standard dynamics studies processes in real time, sometimes it also considers discrete dynamical systems. The step of discrete dynamics is in the appropriate category.

In algebraic dynamics one typically studies discrete dynamical systems on algebraic varieties. Such a system is given by a regular endomorphism $D: X\to X$ of a variety $X$.

• L. Szpiro, Algebraic dynamics, pdf

The case over number fields is also called arithmetic dynamics, see

• wikipedia arithmetic dynamics