Title: Rational Billiards, translation surfaces and ergodicity
Speaker: Professor Howard Masur
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:
An appealing example of a dynamical system is given by billiards in a polygon in the plane. An important class of polygonal billiards are those for which the vertex angles are multiples of pi. For these billiard tables there is a 1 parameter family of dynamical systems, one for each direction. A standard unfolding process turns the polygon into what is called a translation surface and the billiard flow becomes a directional flow by straight lines on the surface. There is an interesting behavior discovered almost 40 years ago of a directional flow on a billiard table such that every orbit is dense but some orbits are not uniformly distributed on the surface. This is called a failure of unique ergodicity. I will introduce the notion of unique ergodicity and survey some of the progress made in understanding rational billiards.Date: Friday, May 08, 2009