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KAM theory: The legacy of Kolmogorov's 1954 paper

Author: Henk W. Broer
Translated by:
Journal: Bull. Amer. Math. Soc. 41 (2004), 507-521
MSC (2000): Primary 37C55, 37C70, 37A60, 34C15
Published electronically: February 9, 2004
MathSciNet review: 2083638
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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.

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Henk W. Broer
Affiliation: Department of Mathematics and Computing Science, University of Groningen, Blauwborgje 3, NL-9747 AC, Groningen, The Netherlands

Received by editor(s): November 18, 2003
Received by editor(s) in revised form: December 16, 2003
Published electronically: February 9, 2004
Article copyright: © Copyright 2004 American Mathematical Society