Topological entropy and recurrence properties in non-autonomous dynamical systems

TL;DR

This paper investigates topological entropy and recurrence in non-autonomous dynamical systems, introducing pseudo-entropy concepts and proving their equivalence to topological entropy.

Contribution

It introduces pseudo-entropy and periodic-pseudo-entropy for non-autonomous systems and establishes their equivalence with topological entropy.

Findings

Pseudo-entropy equals topological entropy in non-autonomous systems

Periodic-pseudo-entropy is equivalent to topological entropy

Provides new tools for analyzing recurrence in dynamical systems

Abstract

In this paper we study topological entropy and recurrence properties of non-autonomous dynamical system generated by a family of continuous self maps on a compact space X. Specially, we introduce the pseudo-entropy and periodic-pseudo-entropy and prove their equivalence with the topological entropy for non-autonomous dynamical systems.