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arXiv · 1401.7099

The classical KAM theorem for Hamiltonian systems via rational approximations

Abed Bounemoura·Stephane Fischler
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Abstract

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-R\"ussmann 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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Abed Bounemoura, Stephane Fischler. 2014-01-28. The classical KAM theorem for Hamiltonian systems via rational approximations. https://doi.org/10.1134/s1560354714020087

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