## EVENT DETAILS AND ABSTRACT

**Colloquium**
**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

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Jeff Xia

**Contact email:** xia@math.northwestern.edu

**Contact Phone:** 847-491-5487

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