Entropy, pseudo-orbit tracing property and positively expansive measures

TL;DR

This paper investigates the relationship between entropy and positively expansive measures in homeomorphisms with the pseudo-orbit tracing property, showing that positive entropy follows from the existence of such measures.

Contribution

It establishes a link between positively expansive measures and positive topological entropy for systems with the pseudo-orbit tracing property.

Findings

Positively expansive measures imply positive topological entropy.

The pseudo-orbit tracing property is crucial for the main result.

Applications demonstrate the relevance of the theoretical findings.

Abstract

We study homeomorphisms of compact metric spaces whose restriction to the nonwandering set has the pseudo-orbit tracing property. We prove that if there are positively expansive measures, then the topological entropy is positive. Some short applications of this result are included.