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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

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00937185
Date
2014
Journal name
Regular and Chaotic Dynamics
Volume
19
Number
2
Publisher
Springer
Pages
251-265
Publication identifier
Metadata
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Author(s)
Fischler, Stephane
Bounemoura, Abed
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 / Keywords
Hamiltonian systems; KAM theorem