Variational principle for neutralized Bowen topological entropy

TL;DR

This paper introduces a new concept of neutralized Bowen topological entropy for subsets in dynamical systems and establishes variational principles relating it to local and Katok's entropies.

Contribution

It defines neutralized Bowen topological entropy and proves variational principles connecting it with existing entropy notions.

Findings

Established variational principles for neutralized Bowen topological entropy.

Connected neutralized Bowen entropy with Brin-Katok local entropy.

Linked neutralized Bowen entropy to neutralized Katok's entropy.

Abstract

Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as $$B_n(x,e^{-n\epsilon})=\{y\in X: d(T^jx, T^jy)<e^{-n\epsilon}, \forall 0\leq j\leq n-1\}.$$ We introduce the notion of neutralized Bowen topological entropy of subsets by neutralized Bowen open ball, and establish variational principles for neutralized Bowen topological entropy of compact subsets in terms of neutralized Brin-Katok local entropy and neutralized Katok's entropy.