## EVENT DETAILS AND ABSTRACT

**Colloquium**
**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.

**Date:** Friday, October 8, 1999

**Time:** 4:30pm

**Where:** Annenberg G15

**Contact Person:** Prof. Gui-Qiang Chen

**Contact email:** gqchen@math.nwu.edu

**Contact Phone:** 847-491-5553

Copyright © 1997-2024
Department of Mathematics, Northwestern University.