**Contemporary Mathematics**

Volume: 567;
2012;
264 pp;
Softcover

MSC: Primary 37; 20; 22;

Print ISBN: 978-0-8218-6922-2

Product Code: CONM/567

List Price: $99.00

AMS Member Price: $79.20

MAA Member Price: $89.10

**Electronic ISBN: 978-0-8218-8539-0
Product Code: CONM/567.E**

List Price: $99.00

AMS Member Price: $79.20

MAA Member Price: $89.10

# Dynamical Systems and Group Actions

Share this page *Edited by *
*Lewis Bowen; Rostislav Grigorchuk; Yaroslav Vorobets*

This volume contains cutting-edge research from leading experts in ergodic theory, dynamical systems and group actions. A large part of the volume addresses various aspects of ergodic theory of general group actions including local entropy theory, universal minimal spaces, minimal models and rank one transformations. Other papers deal with interval exchange transformations, hyperbolic dynamics, transfer operators, amenable actions and group actions on graphs.

#### Readership

Graduate students and research mathematicians interested in ergodic theory, dynamical systems, and group actions.

# Table of Contents

## Dynamical Systems and Group Actions

- Preface ix10 free
- Bibliography xi12 free
- Hyperfinite actions on countable sets and probability measure spaces 114 free
- A road to the spectral radius of transfer operators 1730
- 1. Introduction 1831
- 2. Reversible dynamics. Spectral radius and ergodic measures 1932
- 3. Irreversible-reversible dynamics 2235
- 4. Irreversible dynamics. Weighted shifts and Perron–Frobenius operators. Spectral radius and entropy 2336
- 5. Spectral potential of a transfer operator. Convexity, Legendre duality and thermodynamics 2740
- 6. Spectral potentials and dual entropy 3346
- 7. 𝑡-entropy and variational principle for transfer operators 3447
- 8. Properties of 𝑡-entropy. Entropy Statistic Theorem and Variational Principle for 𝑡-entropy 3649
- 9. Variational principle for weighted shift operators 3750
- 10. Multiterm functional operators. Variational principles etc. 3952
- References 4760

- A condition for weak mixing of induced IETs 5366
- Every countably infinite group is almost Ornstein 6780
- Fair dice-like hyperbolic systems 7992
- Complexity and heights of tori 89102
- Flows with uncountable but meager group of self-similarities 99112
- The universal minimal space of the homeomorphism group of a h-homogeneous space 105118
- Generic eigenvalues, generic factors and weak disjointness 119132
- Around King’s rank-one theorems: Flows and ℤⁿ-actions 143156
- 1. Introduction 143156
- 2. Preliminaries and notations 144157
- 3. Rank-one flows 145158
- 4. Approximation theorem 148161
- 5. Weak closure theorem for rank-one flows 150163
- 6. Rigidity of factors of rank-one flows 152165
- 7. King’s theorem for flat-roof rank-one flow 155168
- 8. ℤⁿ-Rank-one action 157170
- References 160173

- Random walks on random horospheric products 163176
- Statistics of gaps in the sequence {√𝑛} 185198
- Invariant distributions for interval exchange transformations 191204
- 1. Introduction 191204
- 2. The spaces ℒ(𝒯) and 𝒵(𝒯) 194207
- 3. Finitely additive invariant measures and coboundaries 201214
- 4. ℒ(𝒯) and invariant distributions 204217
- 5. Zippered rectangles flow 207220
- 6. Multiplicative coboundaries 209222
- 7. The Kontsevich-Zorich cocycle 211224
- 8. The Rauzy cocycle 213226
- References 218231

- Notes on the Schreier graphs of the Grigorchuk group 221234
- Minimal models for free actions 249262