PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mari Royer, Yakov Pesin, Anatole Katok, Svetlana Katok, Dmitri Burago.

Title:The Existence of Elliptic Periodic Orbits in the Smoothed Bunimovich stadium
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Sherry Teti, Bryn Mawr
Abstract:
A general question of interest in billiards is to determine whether a given billiard is ergodic or nonergodic. The celebrated Bunimovich stadium is an example of a nonsmooth billiard region whose billiard motion is ergodic. Question: Does a convex C^{infinity}-smooth deformation of the Bunimovich stadium remain an ergodic system? In stadiums of both short and arbitrarily long lengths, the existence of elliptic periodic orbits is demonstrated. Corresponding to these orbits, a continuum of length values is also demonstrated. It is a widely accepted belief that elliptic periodic orbits are generically stable, implying nonergodicity of the modified billiard system. These results may suggest the falsity of the Boltzmann Hypothesis (in its original general form).

Room Reservation Information

Room Number:MB106
Date:02 / 02 / 2009
Time:03:30pm - 05:30pm