- Series
- CDSNS Colloquium
- Time
- Monday, September 29, 2014 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Marcel Guardia – Univ. Polit. Catalunya
- Organizer
- Rafael de la Llave
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.