For more information about this meeting, contact Mari Royer, Yakov Pesin, Anatole Katok, Svetlana Katok, Dmitri Burago.
|Title:||On a simpler proof of the invariant torus theorem in KAM theory|
|Seminar:||Center for Dynamics and Geometry Seminars|
|Speaker:||Jacques Fejoz, Paris 6 and Observatoire de Paris|
|Under some non degeneracy condition of the Hamiltonian, this theorem
asserts that a diophantine, quasiperiodic, invariant Lagrangian torus
persists under small perturbations of the Hamiltonian.
There are many proofs of this theorem. All of them are rendered
difficult by the presence of small denominators, which prevents from
using the usual inverse function theorem in Banach spaces.
I will sketch a proof in the category of real analytic Hamiltonians,
which simplifies and combines Zehnder's and Herman's approaches. In
particular, very explicit bounds for the perturbation are obtained.|
Room Reservation Information
|Date:||02 / 25 / 2009|
|Time:||03:30pm - 05:30pm|