The classical KAM theorem for Hamiltonian systems via rational approximations
Dynamical Systems
2015-06-18 v1
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.
Cite
@article{arxiv.1401.7099,
title = {The classical KAM theorem for Hamiltonian systems via rational approximations},
author = {Abed Bounemoura and Stephane Fischler},
journal= {arXiv preprint arXiv:1401.7099},
year = {2015}
}