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Local Entropy Theory of a Random Dynamical System

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Local Entropy Theory of a Random Dynamical System Synopsis

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.

About This Edition

ISBN: 9781470410551
Publication date:
Author: Anthony H Dooley, Guohua Zhang
Publisher: American Mathematical Society
Format: Paperback
Pagination: 106 pages
Series: Memoirs of the American Mathematical Society
Genres: Probability and statistics