• Corpus ID: 224803194

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

  title={Non-existence of a universal zero entropy system for non-periodic amenable group actions},
  author={Georgii Veprev},
  journal={arXiv: Dynamical Systems},
  • G. Veprev
  • Published 19 October 2020
  • Mathematics
  • arXiv: Dynamical Systems
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 $G = \mathbb{Z}$. 

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