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Article Dans Une Revue Regular and Chaotic Dynamics Année : 2014

The classical KAM theorem for Hamiltonian systems via rational approximations

Résumé

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.
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hal-00937185 , version 1 (28-01-2014)

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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⟩
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