EVENT DETAILS AND ABSTRACT

Title: Periodic Orbits for Rational Billiards and Flat Surfaces
Speaker: Professor Howard Masur
Speaker Info: University of Illinois at Chicago
Brief Description:
Special Note: Special Time and Place! Joint with Midwest Dynamical Systems Seminar
Abstract:

It is a well-known fact that the number of integer lattice points (p,q) inside a circle of radius R grows asymptotically like \pi R^2. The number of primitive lattice point; those for which p and q are relatively prime grows asymptotically like \pi R^2/zeta(2). This is equivalent to the growth rate for the number of (parallel families of) simple closed geodesics on the flat torus and in turn this is the growth rate for the number of (parallel families of) periodic orbits for billiards in a square. We consider more generally billiards in polygons whose vertex angles are rational multiples of \pi. In 1989 Veech found examples of rational billiards for which one can find asymptotic growth rates. I will discuss Veech's examples and more recent work that it has inspired.