Variational principle for neutralized Bowen topological entropy on subsets of non-autonomous dynamical systems

TL;DR

This paper extends the concept of neutralized Bowen topological entropy to non-autonomous dynamical systems, establishing variational principles that connect topological entropy with measure-theoretic entropies.

Contribution

It introduces new notions of neutralized entropy for non-autonomous systems and proves variational principles linking these to measure-theoretic entropies, extending prior autonomous system results.

Findings

Defined neutralized Bowen topological entropy for non-autonomous systems

Proved variational principles relating topological and measure-theoretic entropies

Extended autonomous system results to non-autonomous settings

Abstract

Ovadia and Rodriguez-Hertz (Neutralized local entropy, arXiv:2302.10874) defined the neutralized Bowen open ball for an autonomous dynamical system on a compact metric space. Replacing the usual Bowen open ball with neutralized Bowen open ball, we introduce the notions of neutralized Bowen topological entropy of subsets, neutralized weighted Bowen topological entropy of subsets, lower neutralized Brin-Katok's local entropy of Borel probability measures, and neutralized Katok's entropy of Borel probability measures for a non-autonomous dynamical system on a compact metric space. Then, we establish variational principles for neutralized Bowen topological entropy and neutralized weighted Bowen topological entropy of non-empty compact subsets in terms of lower neutralized Brin-Katok's local entropy and neutralized Katok's entropy. In particular, this extends the main result of (YANG, R., CHEN, E., ZHOU, X.: Variational principle for neutralized Bowen topological entropy, arXiv:2303.01738v1) for autonomous dynamical systems.