Event Type:

Department Colloquium

Date/Time:

Friday, March 16, 2007 - 08:00

Location:

Kidd 364

Guest Speaker:

Institution:

San Francisco State U.

Abstract:

Let P be a polygon whose angles are rational multiples of pi. A direction is said to be minimal (resp. uniquely ergodic) if every billiard trajectory with the prescribed initial direction is dense (resp. uniformly distributed.)

Veech discovered a class of polygons, which includes all the regular n-gons, with the property that every minimal direction is uniquely ergodic. He also showed that there are polygons (2-by-1 rectangle with a barrier down the middle of irrational length) that do not have this property, i.e. they admit dense but not uniformly distributed trajectories.

In this talk, I will describe some joint work with Howard Masur and Pascal Hubert that allow us to give further examples of polygons that admits minimal non-uniquely ergodic directions.