eBook ISBN:  9781470419677 
Product Code:  MEMO/233/1099.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $45.00 
eBook ISBN:  9781470419677 
Product Code:  MEMO/233/1099.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $45.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 233; 2014; 106 ppMSC: Primary 37
In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of \(\mathbb{R}\) or \(\mathbb{N}\) is replaced by the action of an infinite countable discrete amenable group.
Given such a system, and a monotone subadditive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measuretheoretic entropy. They also discuss some variants of this variational principle.
The authors introduce both topological and measuretheoretic 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

Chapters

1. Introduction

1. Preliminaries

2. Infinite countable discrete amenable groups

3. Measurable dynamical systems

4. Continuous bundle random dynamical systems

2. A Local Variational Principle for Fiber Topological Pressure

5. Local fiber topological pressure

6. Factor excellent and good covers

7. A variational principle for local fiber topological pressure

8. Proof of main result Theorem

9. Assumption $(\spadesuit )$ on the family $\mathbf {D}$

10. The local variational principle for amenable groups admitting a tiling Følner sequence

11. Another version of the local variational principle

3. Applications of the Local Variational Principle

12. Entropy tuples for a continuous bundle random dynamical system

13. Applications to topological dynamical systems


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In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of \(\mathbb{R}\) or \(\mathbb{N}\) is replaced by the action of an infinite countable discrete amenable group.
Given such a system, and a monotone subadditive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measuretheoretic entropy. They also discuss some variants of this variational principle.
The authors introduce both topological and measuretheoretic 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.

Chapters

1. Introduction

1. Preliminaries

2. Infinite countable discrete amenable groups

3. Measurable dynamical systems

4. Continuous bundle random dynamical systems

2. A Local Variational Principle for Fiber Topological Pressure

5. Local fiber topological pressure

6. Factor excellent and good covers

7. A variational principle for local fiber topological pressure

8. Proof of main result Theorem

9. Assumption $(\spadesuit )$ on the family $\mathbf {D}$

10. The local variational principle for amenable groups admitting a tiling Følner sequence

11. Another version of the local variational principle

3. Applications of the Local Variational Principle

12. Entropy tuples for a continuous bundle random dynamical system

13. Applications to topological dynamical systems