[CvGmt News] Avviso Colloquium di Matematica - Prof. Vadim Kaloshin

[Alfonso Sorrentino]

COLLOQUIUM DI MATEMATICA

Titolo: Arnold Diffusion via Invariant Cylinders and Mather Variational Method

Relatore: Prof. Vadim Kaloshin
(University of Maryland, USA)

Mercoledi' 16 Aprile 2014 ORE 16:00

Aula F,
Dipartimento di Matematica e Fisica,
Universita' di Roma Tre,
L.go S. L. Murialdo 1


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 one with K. Zhang and one with M. Guardia we prove strong form of
Arnold's conjecture in dimension n=3.

Riferimento: Alfonso Sorrentino