Non-existence of a universal zero entropy system for non-periodic amenable group actions

2020/10/19 by Georgii Veprev, Veprev, Georgii
Mathematics · #28D15 #28D20 #37A15 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2010.09806

openalex publication_date 2020/10/19 · openalex created_date 2022/10/21 · openalex updated_date 2026/07/28

Abstract

Let G be a non-periodic amenable group. We prove that there does not exist a topological action of G for which the set of ergodic invariant measures coincides with the set of all ergodic measure-theoretic G-systems of entropy zero. Previously J. Serafin, answering a question by B. Weiss, proved the same for G = ℤ.

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