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Home > Mathematics and Science Textbooks > Mathematics > Probability and statistics > Local Entropy Theory of a Random Dynamical System: (Memoirs of the American Mathematical Society)
Local Entropy Theory of a Random Dynamical System: (Memoirs of the American Mathematical Society)

Local Entropy Theory of a Random Dynamical System: (Memoirs of the American Mathematical Society)


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About the Book

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.

Table of Contents:
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

About the Author :
Anthony H. Dooley, University of Bath, United Kingdom. Guohua Zhang, Fudan University, Shanghai, People's Republic of China.


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Product Details
  • ISBN-13: 9781470410551
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Height: 254 mm
  • No of Pages: 106
  • Weight: 200 gr
  • ISBN-10: 1470410559
  • Publisher Date: 30 Jan 2015
  • Binding: Paperback
  • Language: English
  • Series Title: Memoirs of the American Mathematical Society
  • Width: 178 mm


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