Events

An orientation preserving piecewise isometry T is a collection of two or more rotations or translations defined on mutually disjoint polygonal domains in the plane. Iteration of T leads to behavior that is intriguing and beautiful, especially as seen through the graphics of a partition into cells which do not get broken up by the iteration process. Despite twenty year efforts to understand the dynamics of T, we are far from a thorough understanding it. In this talk I will attempt to engage audience to use their intuition from classical continuous dynamics in order to derive a few results about the dynamics of T. In particular we will focus on the dynamics of a cone-strip exchange and use basic measure arguments. This series of occasional seminars is intended for those interested in Nonlinear Dynamics and Dynamical Systems who have Access Grid facilities (as used in the MAGIC network).

We will present two results in mathematical physics which can be obtained as applications of a result in homogeneous dynamics. The first result concern the dynamics in a class of pseudo-integrable billiards in ellipses, i.e. elliptical billiards with a vertical barrier. The other the behaviour of light rays in arrays of perfect retroreflectors, also known as Eaton lenses. Both results are based on an equidistribution result in the space of affine lattices, that guarantees that typical points on certain curves are Birkhoff generic. The talk is based on joint work with Krzysztof Fraczek and Ronggang Shi.