PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Federico Rodriguez Hertz, Stephanie Zerby, Anatole Katok, Boris Kalinin, Dmitri Burago.

Title:Arnold Diffusion via Invariant Cylinders and Mather Variational Method
Seminar:Center for Dynamics and Geometry Seminars
Speaker:Vadim Kaloshin, University of Maryland TWO HOUR TALK
Abstract:
The famous ergodic hypothesis claims that a typical Hamiltonian dynamics on a typical energy surface is ergodic. However, KAM theory disproves this. It establishes a persistent set of positive measure of invariant KAM tori. The (weaker) quasi-ergodic hypothesis, proposed by Ehrenfest and Birkhoff, says that a typical Hamiltonian dynamics on a typical energy surface has a dense orbit. This question is wide open. In early 60th Arnold constructed an example of instabilities for a nearly integrable Hamiltonian of dimension $n>2$ and conjectured that this is a generic phenomenon, nowadays, called Arnold diffusion. In the last two decades a variety of powerful techniques to attack this problem were developed. In particular, Mather discovered a large class of invariant sets and a delicate variational technique to shadow them. In a series of preprints: one joint with P. Bernard, K. Zhang and two with K. Zhang we prove Arnold's conjecture in dimension $n=3$.

Room Reservation Information

Room Number:MB114
Date:04 / 29 / 2013
Time:03:35pm - 05:35pm