Low Complexity Dynamics (08w5046)

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.