Foreword

Summary

This volume owes its existence to the Clay Mathematics Institute /Mathematical Sciences Research Institute Workshop on “Recent Progress in Dynamics”, held at the Mathematical Sciences Research Institute for a week in late September to early October 2004. This is not a proceedings volume, but most authors were participants of the workshop, and the two lead surveys reflect a good deal of what David Fisher and Helmut Hofer presented during their workshop talks.

The workshop represented a broad array of dynamical systems, not least in order to reflect the breadth of taste exhibited by Anatole Katok, whose sixtieth birthday was observed during the workshop. This was possible because we were able to invite a great number of participants from near and far, and the essential ingredient in making this possible was the generous financial support from the Clay Mathematics Institute and the Mathematical Sciences Research Institute (which is in turn supported by the National Science Foundation), as well as from the Pennsylvania State University and Tufts University. As the host of the workshop, the Mathematical Sciences Research Institute also provided administrative support for the organizers and participants. It is a pleasure to acknowledge this support.

Funding alone does not produce a successful workshop, and I want to thank my fellow workshop organizers Michael Brin, Gregory Margulis, Yakov Pesin, Peter Sarnak, Klaus Schmidt, Ralf Spatzier and Robert Zimmer. Foremost among these was Yakov Pesin, whose involvement was constant and most valuable. And a successful workshop does not by itself lead to written works of interest, so I wish to thank the authors of the articles in this volume for their contributions. Thanks also go to Silvio Levy for his smooth handling of the entire production process, and to Kathleen Hasselblatt for her support.

The aim of the workshop and this volume is to impact the development of dynamical systems, and to that end we paid some attention to making it possible for younger participants to attend the workshop, and the surveys in this volume may attract young mathematicians to those subject areas. The Mathematical Sciences Research Institute adds to the impact of the event by maintaining streaming video of the lectures given at the workshop, which enables everyone to view these lectures (see http://www.msri.org/calendar/workshops/WorkshopInfo/267/show_workshop). Finally, a problem list in this volume is hoped to inspire research into subjects that posed challenges at the time of the workshop. I hope that the readers will find this volume interesting, useful and inspiring.