Speaker
Description
Consider a small amplitude perturbation of an analytic integrable Hamiltonian system: Nekhoroshev theorem ensures that, if the unperturbed part of the Hamiltonian fulfills a suitable non-degeneracy assumption, known in literature as steepness, all the actions are quasi-preserved for time scales that are exponentially long in the perturbative parameter.
What happens when the perturbative term in the Hamiltonian is also allowed to depend on time ?
We study the case of time quasi-periodic perturbations and we prove that a Nekhoroshev type result still holds, under the assumption that the system fulfills a different non-degeneracy condition, originally introduced by Nekhoroshev and called P-steepness. Our approach is based on an extension to the time dependent case of the construction exhibited by Guzzo, Chierchia and Benettin in their proof of classical Nekhoroshev theorem. One of the main difficulties is to deal with the more complex geometry of resonances of the time dependent case. This talk is based on a joint work with D. Bambusi, S. Barbieri, and M. Giralt.