# The Classical KAM Theorem for Hamiltonian Systems via Rational Approximations

*2014, Volume 19, Number 2, pp. 251-265*

Author(s):

**Bounemoura A., Fischler S.**

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 [4] for perturbations of constant vector fields on the torus.

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