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Variational principle for neutralized Bowen topological entropy

Rui Yang, Ercai Chen, Xiaoyao Zhou

TL;DR

The notion of neutralized Bowen topological entropy of subsets of compact subsets is introduced in this note and variational principles for neutralization Bowen topologically entropy of Compact subsets in terms ofneutralized Brin-Katok local entropy and neutralized Katok's entropy are established.

Abstract

Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as $$B_n(x,e^{-nε})=\{y\in X: d(T^jx, T^jy)<e^{-nε}, \forall 0\leq j\leq n-1\}.$$ 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.

Variational principle for neutralized Bowen topological entropy

TL;DR

The notion of neutralized Bowen topological entropy of subsets of compact subsets is introduced in this note and variational principles for neutralization Bowen topologically entropy of Compact subsets in terms ofneutralized Brin-Katok local entropy and neutralized Katok's entropy are established.

Abstract

Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as 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.
Paper Structure (6 sections, 10 theorems, 59 equations)

This paper contains 6 sections, 10 theorems, 59 equations.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Neutralized topological entropies of subsets
  4. Lower neutralized Brin-Katok local entropy
  5. Neutralized Katok's entropy
  6. Proof of Theorem 1.1

Key Result

Theorem 1.1

Let $(X,T)$ be a TDS and $K$ be a non-empty compact subset of $X$. Then where $h_{top}^{\widetilde{B}}(T,K)$ denotes neutralized Bowen topological entropy of $K$, and $\underline{h}_{\mu}^{\widetilde{BK}}(T,\epsilon), h_{\mu}^{\widetilde{K}}(T,\epsilon)$ are lower neutralized Brin-Katok local entropy of $\mu$, neutralized Katok entropy of $\mu$, respectively.

Theorems & Definitions (29)

  • Theorem 1.1
  • Proposition 2.1
  • proof
  • Definition 2.2
  • Proposition 2.3
  • proof
  • Definition 2.4
  • Proposition 2.5
  • proof
  • Proposition 2.6
  • ...and 19 more