January 2014 February 2014 March 2014 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 1 5 6 7 8 9 10 11 2 3 4 5 6 7 8 2 3 4 5 6 7 8 12 13 14 15 16 17 18 9 10 11 12 13 14 15 9 10 11 12 13 14 15 19 20 21 22 23 24 25 16 17 18 19 20 21 22 16 17 18 19 20 21 22 26 27 28 29 30 31 23 24 25 26 27 28 23 24 25 26 27 28 29 30 31 |

4:00 pm Thursday, February 20, 2014 Colloquium: Arnold Diffusion via Invariant Cylinders and Mather Variational Methodby Vadim Kaloshin (University of Maryland) in HB 227- 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 one with K. Zhang and one with M. Guardia we prove strong form of Arnold's conjecture in dimension n=3.
Submitted by milivoje.lukic@rice.edu |