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A variational principle for entropy of a random dynamical system

Yuan Lian

Abstract

In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable fiber entropy of a random dynamical system.

A variational principle for entropy of a random dynamical system

Abstract

In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable fiber entropy of a random dynamical system.
Paper Structure (3 sections, 3 theorems, 59 equations)

This paper contains 3 sections, 3 theorems, 59 equations.

Table of Contents

  1. introduction
  2. Preliminaries
  3. Main result

Key Result

Lemma 2.4

Let $\mathbf{F}$ be a RDS associated to $G-$action. For any $F\in \mathcal{F}(G)$ and a positive real number $\varepsilon$, the function $Sep(\omega ,F,\varepsilon,\mathbf{F})$ is measurable in $\omega$, and for each $\delta>0$ there exists a family of maximal $(\omega,F,\varepsilon,\mathbf{F})$ sep where $\sharp(L_{\omega})$ denote the cardinality of $G_{\omega}$ and measurable in $\omega$ (in th

Theorems & Definitions (9)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Lemma 2.4
  • proof
  • Definition 2.5
  • Proposition 2.1
  • Proposition 3.1
  • proof