Non-existence of a universal zero entropy system via generic actions of almost complete growth
Dynamical Systems
2022-09-07 v1
Abstract
We prove that a generic p.m.p. action of a countable amenable group has scaling entropy that can not be dominated by a given rate of growth. As a corollary, we obtain that there does not exist a topological action of for which the set of ergodic invariant measures coincides with the set of all ergodic p.m.p. -systems of entropy zero. We also prove that a generic action of a residually finite amenable group has scaling entropy that can not be bounded from below by a given sequence. We also show an example of an amenable group that has such lower bound for every free p.m.p. action.
Keywords
Cite
@article{arxiv.2209.01902,
title = {Non-existence of a universal zero entropy system via generic actions of almost complete growth},
author = {Georgii Veprev},
journal= {arXiv preprint arXiv:2209.01902},
year = {2022}
}