Descriptive Set Theory and Dynamical Systems

doi:10.1017/CBO9781107325999

In recent years there has been a growing interest in the interactions between descriptive set theory and various aspects of the theory of dynamical systems, including ergodic theory and topological dynamics. This volume, first published in 2000, contains a collection of survey papers by leading researchers covering a wide variety of recent developments in these subjects and their interconnections. This book provides researchers and graduate students interested in either of these areas with a guide to work done in the other, as well as with an introduction to problems and research directions arising from their interconnections.

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Descriptive Set Theory and Dynamical Systems

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - An Overview of Infinite Ergodic Theory
pp 1-30

2 - The Multifarious Poincaré Recurrence Theorem
pp 31-58

3 - Groups of Automorphisms of Measure Space and Weak Equivalence of Cocycles
pp 59-86

4 - A Descriptive View of Ergodic Theory
pp 87-172

5 - Structure Theory as a Tool in Topological Dynamics
pp 173-210

6 - Orbit Properties of Pseudo-homeomorphism Groups of a Perfect Polish Space and their Cocycles
pp 211-230

7 - Descriptive Dynamics
pp 231-258

8 - Polish Groupoids
pp 259-272

9 - A Survey of Generic Dynamics
pp 273-291

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Descriptive Set Theory and Dynamical Systems

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