Preface

Summary

During July 1-5, 1996 an International Workshop on Descriptive Set Theory and Dynamical Systems took place at the Centre International de Rencontres Mathématiques (CIRM) of Marseille-Luminy, France. The aim of this meeting was to bring together mathematicians interested in these two areas and their interrelationships. The idea came out of this, very successful, conference to put together a collection of survey papers related to these fields, and their growing interactions, that would be accessible to a wide audience of students and researchers. The present volume is the realization of this idea.

The contributions provide introductions to a broad spectrum of topics and are meant to guide the reader to the most recent developments in many active areas of research. Here is a bird's eye view of the subjects covered here:

1. 1) J. Aaronson: ergodic theory of non-singular transformations with particular emphasis on transformations admitting σ-finite infinite invariant measures.

2. 2) V. Bergelson: recurrence theorems in ergodic theory and their applications in combinatorics.

3. 3) S. Bezuglyi: structure of cocycles for non-singular group actions.

4. 4) M. Foreman: descriptive aspects of ergodic theory.

5. 5) E. Glasner: topological dynamics with particular emphasis on the structure theory of minimal dynamical systems and its applications.

6. 6) V. Ya. Golodets, V. M. Kulagin, and S.D. Sinel'shchikov: cocycles in generic topological dynamics.

7. 7) A.S. Kechris: the descriptive theory of Polish group actions.

8. 8) A. B. Ramsay: aspects of the theory of groupoids.

9. 9) B. Weiss: survey of topics in generic dynamics.