Uniformly distributed periodic orbits of endomorphisms on $n$-tori
Dynamical Systems
2024-11-19 v2
Abstract
We prove that any ergodic endomorphism on torus admits a sequence of periodic orbits uniformly distributed in the metric sense. As a corollary, an endomorphism on torus is ergodic if and only if the Haar measure can be approximated by periodic measures.
Cite
@article{arxiv.2407.19665,
title = {Uniformly distributed periodic orbits of endomorphisms on $n$-tori},
author = {Daohua Yu and Shaobo Gan},
journal= {arXiv preprint arXiv:2407.19665},
year = {2024}
}