Rational billiards, Fuchsian groups and ergodic theory

Howard Masur

University of Illinois at Chicago

Brandeis University

Thursday, February 1, 2007

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: An interesting example of a dynamical system is given by billiards in a polygon in the plane. An important special case is if the vertex angles are rational multiples of pi. A standard unfolding process leads to a flow on what is called a translation surface. A classical case is the linear flow on a flat torus. It turns out that one often gets information about the flow on the individual surface by studying a different dynamical system; namely the action of the group SL(2,R) on families or moduli spaces of surfaces. If the stabilizer of a point by this action is a lattice in SL(2,R) then the surface is called a Veech surface. If the surface is a Veech surface, then the flows on that surface have nice dynamics. We will discuss this whole set-up and developments in the subject over the last several years.

Home Web page: Alexandru I. Suciu Posted: January 9, 2007
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