KAM theory: The legacy of Kolmogorov's 1954 paper

Henk W. Broer

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    Abstract

    Kolmogorov-Arnold-Moser (or KAM) theory was developed for conservative dynamical systems that are nearly integrable. Integrable systems in their phase space usually contain lots of invariant tori, and KAM theory establishes persistence results for such tori, which carry quasi-periodic motions. We sketch this theory, which begins with Kolmogorov's pioneering work.
    Original languageEnglish
    Pages (from-to)507-521
    Number of pages15
    JournalBulletin of the american mathematical society
    Volume41
    Issue number4
    Publication statusPublished - 2004

    Keywords

    • SMALL DIVISOR PROBLEMS
    • IMPLICIT FUNCTION THEOREMS
    • LOWER-DIMENSIONAL TORI
    • HAMILTONIAN-SYSTEMS
    • TURBULENCE
    • DIFFEOMORPHISMS
    • OSCILLATORS
    • DIFFUSION
    • MOTIONS
    • CIRCLE

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