Uniformly distributed periodic orbits of endomorphisms on n-tori

2024/07/29 by Yu, Daohua, Gan, Shaobo
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.19665

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.

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