Dynamics of foliations, groups and pseudogroupsFoliations,小组和Pseudogroups动力学

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作者： Pawel Walczak 著

出版社：

出版时间： 2004-6-1字数：版次： 1页数： 225印刷时间： 2004/06/01开本： 16开印次： 1纸张：胶版纸I S B N ： 9783764370916包装：精装内容简介

Foliations, groups and pseudogroups are objects which are closely related via the notion of holonomy. In the 1980s they became considered as general dynamical systems. This book deals with their dynamics. Since "dynamics is a very extensive term, we focus on some of its aspects only. Roughly speaking, we concentrate on notions and results related to different ways of measuring complexity of the systems under consideration. More precisely, we deal with different types of growth, entropies and dimensions of limiting objects. Invented in the 1980s (by E. Ghys, R. Langevin and the author) geometric entropy of a foliation is the principal object of interest among all of them.

Throughout the book, the reader will find a good number of inspirating problems related to the topics covered.

Preface

1 Dynamical systems

1.1 Pseudogroups

1.2 First examples

1.3 Foliations, laminations and holonomy

1.4 Markov pseudcgroups

1.5 Hyperbolic spaces and groups

2 Growth

2.1 Growth types

2.2 Growth in groups

2.3 Orbit growth for pseudogroups

2.4 Expansion growth

3 Entropy

3.1 Entrotpy of classical systems

3.1.1 Topological entropy of a transformation

3.1.2 Invariant measures

3.1.3 Measure-theoretic entropy

3.1.4 Examples

3.1.5 Variational principle

3.2 Entropy of pseudogroups

3.3 Geometric entropy of foliations

3.4 Relating various entropies

3.5 Examples and constructions

3.5.1 Pullback

3.5.2 Gluing

3.5.3 Turbulization

3.6 Entropy and resiliency

4 Invariant measures

4.1 Basic definitions and facts

4.2 Transverse invariant measures and homology

4.3 Measures and orbit growth

4.4 Transverse invariant measures in codimension

4.5 Vanishing entropy and invariant measures

4.6 Entropy, geodesic flow and invariant measures

4.7 Harmonic measures

4.8 Patterson-Sullivan measures

5 Hausdorff dimension

5.1 Definitions and basic facts

5.2 Julia sets

5.3 Dimension in foliated manifolds

5.4 Dimension of a hyperbolic boundary

5.5 Dimension of a limit set

6 Varia

6.1 Complexity growth

6.2 Expansive systems

6.3 Pseudo-orbits and pseudoleaves

6.4 Generic leaves

Bibliography

Index