КОЛЛОКВИУМ лаборатории им.П.Л.Чебышева Вторник, 5 марта, 16:00 - 17:00, ауд.14 МИНИКУРС лаборатории им.П.Л.Чебышева Среда, 6 марта, 15:00-17:00, ауд.413 Четверг 7 марта, 15:00-17:00, ауд.413 Матмех, 14 линия ВО, д.29 Vadim Kaloshin (University of Maryland, USA) "Arnold Diffusion via Invariant Cylinders and Mather Variational Method " (joint with P. Bernard, K. Zhang) 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-ergodichypothesis, 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 delicatevariational technique to shadow them. In two preprints: one joint with P. Bernard, K. Zhang and another with K. Zhang we prove Arnold's conjecture in dimension n=3. |