Geometry of KAM tori for nearly integrable Hamiltonian systems

• Autores: Henk W. Broer , Richard Cushman, Francesco Fassò, Floris Takens
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 3, 2007, págs. 725-741
• Idioma: inglés
• DOI: 10.1017/s0143385706000897
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• Resumen

  • We obtain a global version of the Hamiltonian KAM theorem for invariant Lagrangian tori by gluing together local KAM conjugacies with the help of a partition of unity. In this way we find a global Whitney smooth conjugacy between a nearly integrable system and an integrable one. This leads to the preservation of geometry, which allows us to define all non-trivial geometric invariants of an integrable Hamiltonian system (like monodromy) for a nearly integrable one.