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Объявления лаб. Чебышева
by Egor Pifagorov - Tuesday, 26 February 2013, 06:13 PM
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.