Parametric topological entropy on orbits of arbitrary multivalued maps in compact Hausdorff spaces

TL;DR

This paper explores various definitions of parametric topological entropy for orbits of nonautonomous multivalued maps in compact Hausdorff spaces, establishing relationships and extending recent results in this mathematical framework.

Contribution

It introduces a unified analysis of different entropy definitions for multivalued maps and generalizes existing results to a broader setting.

Findings

Relationships between different entropy definitions established

Generalization of recent results to multivalued maps in compact spaces

Extension of entropy concepts to nonautonomous and coincidence orbits

Abstract

The Adler-Konheim-McAndrew type definitions and the Bowen-Dinaburg-Hood type definitions of parametric topological entropy will be considered on orbits and coincidence orbits of nonautonomous multivalued maps in compact Hausdorff spaces. Their mutual relationship and their link to various further types of definitions like those of (parametric) preimage entropy, will be investigated. In this way, several recent results of the other authors will be generalized and extended into a new setting.