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Regular and Chaotic Dynamics

, Volume 19, Issue 2, pp 251–265 | Cite as

The classical KAM theorem for Hamiltonian systems via rational approximations

Article

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 

MSC2010 numbers

37J25 37J40 70H08 70H09 

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.CNRS — CEREMADEUniversité Paris Dauphine Place du Maréchal de Lattre de TassignyParis Cedex 16France
  2. 2.IMCCEObservatoire de ParisParisFrance
  3. 3.Laboratoire de mathématiques d’OrsayUniv Paris SudOrsay CedexFrance

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