A Classical Self-Contained Proof of Kolmogorov’s Theorem on Invariant Tori View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1999

AUTHORS

A. Giorgilli , U. Locatelli

ABSTRACT

The celebrated theorem of Kolmogorov on persistence of invariant tori of a nearly integrable Hamiltonian system is revisited in the light of classical perturbation algorithm. It is shown that the original Kolmogorov’s algorithm can be given the form of a constructive scheme based on expansion in a parameter. A careful analysis of the accumulation of the small divisors shows that it can be controlled geometrically. As a consequence, the proof of convergence is based essentially on Cauchy’s majorants method, with no use of the so called quadratic method. A short comparison with Lindstedt’s series is included. More... »

PAGES

72-89

References to SciGraph publications

  • 1994-07. Twistless KAM tori in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1967-03. Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung in MATHEMATISCHE ANNALEN
  • 1967-03. Convergent series expansions for quasi-periodic motions in MATHEMATISCHE ANNALEN
  • 1997-03. Kolmogorov theorem and classical perturbation theory in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • Book

    TITLE

    Hamiltonian Systems with Three or More Degrees of Freedom

    ISBN

    978-94-010-5968-8
    978-94-011-4673-9

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-94-011-4673-9_8

    DOI

    http://dx.doi.org/10.1007/978-94-011-4673-9_8

    DIMENSIONS

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