Uniformly distributed periodic orbits of endomorphisms on n-tori

2024/07/29 by Daohua Yu, Yu, Daohua, Shaobo Gan +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #Endomorphism #FOS: Mathematics #Geometric and Algebraic Topology #Geometry #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Periodic orbits #Pure mathematics #Quantum chaos and dynamical systems #Torus

paper · pdf · doi:10.48550/arxiv.2407.19665

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/07/29 · openalex created_date 2024/08/01 · openalex updated_date 2026/07/28

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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