# 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} }

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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