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

TL;DR
This paper proves that for non-periodic amenable groups, there is no topological action whose ergodic measures encompass all zero-entropy ergodic systems, extending a previous result from the integers.
Contribution
It generalizes the non-existence of a universal zero-entropy system from the integers to all non-periodic amenable groups.
Findings
No universal zero-entropy system exists for non-periodic amenable groups.
Extends previous results from the integers to broader classes of groups.
Addresses a question posed by B. Weiss.
Abstract
Let be a non-periodic amenable group. We prove that there does not exist a topological action of for which the set of ergodic invariant measures coincides with the set of all ergodic measure-theoretic -systems of entropy zero. Previously J. Serafin, answering a question by B. Weiss, proved the same for .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals
