The classical KAM theorem for Hamiltonian systems via rational approximations
Fischler, Stephane; Bounemoura, Abed (2014), The classical KAM theorem for Hamiltonian systems via rational approximations, Regular and Chaotic Dynamics, 19, 2, p. 251-265. http://dx.doi.org/10.1134/S1560354714020087
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00937185
Journal nameRegular and Chaotic Dynamics
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Abstract (EN)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.
Subjects / KeywordsHamiltonian systems; KAM theorem
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