Effective stability for slow time-dependent near-integrable Hamiltonians and application

Abed Bounemoura (1)

1 IHES - Institut des Hautes Études Scientifiques

The aim of this note is to prove a result of effective stability for a non-autonomous perturbation of an integrable Hamiltonian system, provided that the perturbation depends slowly on time. Then we use this result to clarify and extend a stability result of Giorgilli and Zehnder for a mechanical system with an arbitrary time-dependent potential.

Domaines: Systèmes dynamiques [math.DS]

Abed Bounemoura. Effective stability for slow time-dependent near-integrable Hamiltonians and application. Comptes Rendus. Mathématique, 2013, 351 (17-18), pp.673-676. ⟨hal-00802775⟩