08w5046 Low Complexity Dynamics

Arriving Sunday, May 25 and departing Friday, May 30, 2008

Organizers: Peter Ashwin (University of Exeter), Arek Goetz (San Francisco State University), Anthony Quas (University of Victoria).

Confirmed Participants

Press Release: Low Complexity Dynamics

Information for Participants

Schedule and Abstracts (PDF file)

Final Report (PDF file)

Objectives

The meeting will bring together specialists in interval exchanges, billiards, higher dimensional piecewise isometries, and applications to promote interaction between these groups. The aim would be to encourage cross-fertilization. Over the last couple of years, there have been very significant advances in interval exchanges, leading to the solution of conjectures that have been open and actively studied by many authors for several decades. For this reason, it will be valuable to take stock of the new developments in the field with a view to exporting techniques and paradigms to neighbouring disciplines.

Modeling systems with discontinuities and singularities is becoming increasingly important in applied mathematics. The classes of systems that will form the focus of the meeting are a natural test case: they appear to be tractable, and yet exhibit phenomena that differ from those seen in the hyperbolic setting. The higher dimensional piecewise isometries appear to have a prevalence of periodic behaviour. A key challenge is to assemble a full toolkit for the quantification of this behaviour and also to study the rather subtle aperiodic behaviour.

We plan to organize the conference in such a way as to stimulate discussion among the participants. There will be a relatively small number of lectures (probably around five or six forty-five minute lectures per day) as well as a problem session for which participants will be asked to prepare in advance.