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2013
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# Stéphane Fischler

91405 Orsay Cedex, France
Laboratoire de mathematiques d’Orsay, Univ Paris Sud

## Publications:

 Bounemoura A., Fischler S. The Classical KAM Theorem for Hamiltonian Systems via Rational Approximations 2014, vol. 19, no. 2, pp.  251-265 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–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. Keywords: perturbation of integrable Hamiltonian systems, KAM theory, Diophantine duality, periodic approximations Citation: Bounemoura A., Fischler S.,  The Classical KAM Theorem for Hamiltonian Systems via Rational Approximations, Regular and Chaotic Dynamics, 2014, vol. 19, no. 2, pp. 251-265 DOI:10.1134/S1560354714020087