The Topological Entropy of Stable Sets for Bi-orderable Amenable Groups

Abstract

We study the topological entropy of stable sets for countable discrete infinite bi-orderable amenable group actions. It is shown that in any positive entropy system, there is a measure-theoretically “large” set such that the topological entropy of stable set of any point from the set is no less than the measure-theoretic entropy of the system, moreover the closure of the stable set of any point from the set contains a weak mixing set.