Local entropy theory of a random dynamical system
著者
書誌事項
Local entropy theory of a random dynamical system
（Memoirs of the American Mathematical Society, no. 1099）
American Mathematical Society, c2014
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注記
"volume 233, number 1099 (fifth of 6 numbers), January 2015"
Includes bibliographical references (p. 103-106)
内容説明・目次
内容説明
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.
目次
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
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