Nearly integrable systems with orbits accumulating to KAM tori

Series: 
CDSNS Colloquium
Monday, September 29, 2014 - 11:00
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Univ. Polit. Catalunya
Organizer: 
The quasi-ergodic hypothesis, proposed by Ehrenfest and Birkhoff, says that a typical Hamiltonian system of n degrees of freedom on a typical energy surface has a dense orbit. This question is wide open. In this talk I will explain a recent result by V. Kaloshin and myself which can be seen as a weak form of the quasi-ergodic hypothesis. We prove that a dense set of perturbations of integrable Hamiltonian systems of two and a half degrees of freedom  possess orbits which accumulate in sets of positive measure. In particular, they accumulate in prescribed sets of KAM tori.