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

Georgii Veprev

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

Dynamical Systems 2021-01-01 v3

Authors: Georgii Veprev

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 $G = \mathbb{Z}$ .

Keywords

non-periodic amenable group topological action ergodic invariant measure zero entropy system measure-theoretic dynamical system

Cite

@article{arxiv.2010.09806,
  title  = {Non-existence of a universal zero entropy system for non-periodic amenable group actions},
  author = {Georgii Veprev},
  journal= {arXiv preprint arXiv:2010.09806},
  year   = {2021}
}

Comments

added section 6.3; 20 pages, 1 figure

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