Topological entropy for partial actions of the group $\mathbb Z$

TL;DR

This paper extends the concept of topological entropy to partial actions of the group a5, demonstrating its relation to classical entropy and showing it is concentrated on the non-wandering set.

Contribution

It introduces a new definition of entropy for partial a5-actions, extending classical topological entropy and analyzing its properties.

Findings

Partial entropy generalizes classical topological entropy.

Partial entropy is concentrated on the non-wandering set.

The new definition aligns with existing entropy concepts for full actions.

Abstract

In this paper we introduce the definition of entropy for a partial $\mathbb{Z}$-action. We show that the definition of partial entropy is an extension of the definition of topological entropy for a $\mathbb Z$-action. We also prove that the partial topological entropy is concentrated on the non-wandering set.