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The Lack-of-Parameters Problem in the Kam Theory Revisited

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Hamiltonian Systems with Three or More Degrees of Freedom

Part of the book series: NATO ASI Series ((ASIC,volume 533))

Abstract

We generalize Herman’s method (presented by him at a conference in Lyon in 1990) for constructing invariant n-tori in nearly integrable Hamiltonian systems with N degrees of freedom and degenerate frequency mappings. Whereas M. R. Herman considered the case n = N, we treat the cases n = N and n < N in a unified way. The well-known results by L. H. Eliasson and J. Pöschel on the persistence of elliptic invariant tori in Hamiltonian systems turn out to be particular cases of more general theorems obtained via our approach.

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Author information

Authors and Affiliations

  1. Institute of Energy Problems of Chemical Physics, Lenin prospect 38 Bldg. 2, Moscow, 117829, Russia

    M. B. Sevryuk

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  1. M. B. Sevryuk
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Editor information

Editors and Affiliations

  1. Universitat de Barcelona, Barcelona, Spain

    Carles Simó

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© 1999 Springer Science+Business Media Dordrecht

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Sevryuk, M.B. (1999). The Lack-of-Parameters Problem in the Kam Theory Revisited. In: Simó, C. (eds) Hamiltonian Systems with Three or More Degrees of Freedom. NATO ASI Series, vol 533. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4673-9_79

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  • DOI: https://doi.org/10.1007/978-94-011-4673-9_79

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5968-8

  • Online ISBN: 978-94-011-4673-9

  • eBook Packages: Springer Book Archive

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