KAM theory: The legacy of Kolmogorov’s 1954 paper
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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.References
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Additional Information
- Henk W. Broer
- Affiliation: Department of Mathematics and Computing Science, University of Groningen, Blauwborgje 3, NL-9747 AC, Groningen, The Netherlands
- Email: broer@math.rug.nl
- Received by editor(s): November 18, 2003
- Received by editor(s) in revised form: December 16, 2003
- Published electronically: February 9, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 41 (2004), 507-521
- MSC (2000): Primary 37C55, 37C70, 37A60, 34C15
- DOI: https://doi.org/10.1090/S0273-0979-04-01009-2
- MathSciNet review: 2083638