Local Entropy Theory of a Random Dynamical System

ISBN-13: 9781470410551 / Angielski

Anthony H. Dooley;Guohua Zhang

Opis

In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

Spis treści

• Introduction
• Preliminaries: Infinite countable discrete amenable groups
• Measurable dynamical systems
• Continuous bundle random dynamical systems
• A Local Variational Principle for Fiber Topological Pressure: Local fiber topological pressure
• Factor excellent and good covers
• A variational principle for local fiber topological pressure
• Proof of main result
• Theorem 7.1
• Assumption ª on the family D
• The local variational principle for amenable groups admitting a tiling Folner sequence
• Another version of the local variational principle
• Applications of the Local Variational Principle
• Entropy tuples for a continuous bundle random dynamical system
• Bibliography