Unique ergodicity for zero-entropy dynamical systems with the approximate product property

2019/08/03 by Peng Sun, Sun, Peng
Mathematics · Physics and Astronomy · #37B05 #37B40 #37C40 #37C50 #37E05 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1908.01149

openalex publication_date 2019/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover, we show that unique ergodicity implies the approximate product property if the system has periodic points.

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