• Corpus ID: 224803194

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

@article{Veprev2020NonexistenceOA,
title={Non-existence of a universal zero entropy system for non-periodic amenable group actions},
author={Georgii Veprev},
journal={arXiv: Dynamical Systems},
year={2020}
}
• 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 $G = \mathbb{Z}$.
2 Citations

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