| eBook ISBN: | 978-1-4704-1967-7 |
| Product Code: | MEMO/233/1099.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $45.00 |
| eBook ISBN: | 978-1-4704-1967-7 |
| 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 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
-
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
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
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 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.
-
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
