91405 Orsay Cedex, France
Laboratoire de mathematiques d’Orsay, Univ Paris Sud
Bounemoura A., Fischler S.
The Classical KAM Theorem for Hamiltonian Systems via Rational Approximations
2014, vol. 19, no. 2, pp. 251-265
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  for perturbations of constant vector fields on the torus.