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.
ISBN: | 9781470410551 |
Publication date: | 30th January 2015 |
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 |