%0 Journal Article
%T The classical KAM theorem for Hamiltonian systems via rational approximations
%A Abed Bounemoura
%A Stephane Fischler
%J Mathematics
%D 2014
%I arXiv
%R 10.1134/S1560354714020087
%X 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.
%U http://arxiv.org/abs/1401.7099v1