The Outer Billiard Map
Eugene Gutkin

This is a natural dynamical system associated with any planar
convex, bounded region. If P is the region, the outer billiard on P
is an automorphism of the complement to P. It preserves the Lebesgue
measure and has other nice  features. The character of dynamics reflects
the geometry of P in a subtle way. I will discuss a few results and present
open problems.