Nonexistence of a universal zero entropy system for nonperiodic amenable group actions
Abstract
Let $G$ be a nonperiodic 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 measuretheoretic $G$systems of entropy zero. Previously J. Serafin, answering a question by B. Weiss, proved the same for $G = \mathbb{Z}$.
 Publication:

arXiv eprints
 Pub Date:
 October 2020
 arXiv:
 arXiv:2010.09806
 Bibcode:
 2020arXiv201009806V
 Keywords:

 Mathematics  Dynamical Systems;
 28D15;
 28D20;
 37A15
 EPrint:
 added section 6.3