On periodic orbits of polynomial maps
Dynamical Systems
2023-09-11 v3 Algebraic Geometry
Number Theory
Abstract
We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in arbitrary finitely generated algebraic dynamical systems over fields of characteristic zero.
Cite
@article{arxiv.2305.13529,
title = {On periodic orbits of polynomial maps},
author = {Junho Peter Whang},
journal= {arXiv preprint arXiv:2305.13529},
year = {2023}
}
Comments
7 pages. v3: Extended the main results and improved exposition. Comments are welcome!