Entropy points and applications for free semigroup actions

TL;DR

This paper investigates the local properties of topological entropy in free semigroup actions, demonstrating that entropy points carry full entropy and exploring their fundamental role in system chaos.

Contribution

It introduces the concept of entropy points for free semigroup actions and proves they contain the full entropy, highlighting their significance in chaotic dynamics.

Findings

Entropy points carry the full entropy of the system.

The set of entropy points has important properties related to chaos.

Entropy points are fundamental in understanding local entropy behavior.

Abstract

The aim of this manuscript is to study some local properties of the topological entropy of a free semigroup action. In order to do that we focus on the set of entropy points of a free semigroup action, show that this set carries the full entropy of the system (which, with respect to the chaocity of the system, gives a fundamental relevance to such set) and obtain many interesting properties of such set. Our results are inspired by the ones presented in \cite{YZ}.