The classical KAM theorem for Hamiltonian systems via rational approximations

Abed Bounemoura (1) , Stephane Fischler (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-Rüssmann condition, in real-analytic non-degenerate Hamiltonian systems close to integrable. The proof, which uses rational approximations instead of small divisors estimates, is an adaptation to the Hamiltonian setting of the method we introduced in a previous work for perturbations of constant vector fields on the torus.

Domaines: Systèmes dynamiques [math.DS]

Abed Bounemoura, Stephane Fischler. The classical KAM theorem for Hamiltonian systems via rational approximations. Regular and Chaotic Dynamics, 2014, 19 (2), pp.251-265. ⟨hal-00937185⟩