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Kolmogorov-Arnold-Moser theorem

Can planetary motion be stable?

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Abstract

The contribution of Kolmogorov to classical mechanics is illustrated through the famous Kolmogorov-Arnold-Moser (KAM) theorem. This theorem solves a longstanding problem regarding stability in non-linear Hamiltonian dynamics. Various concepts required to understand the KAM theorem are also developed.

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Suggested Reading

  • A NKolmogorov. Preservation of conditionally periodic movements with small change in the Hamilton function, Los Alamos National Laboratory translation LA-TR-71-67 by Helen Dahlby ofAkad. Nauk. S.S.S.R., Doklady. 98. 527, 1954.

  • The general theory of dynamical systems and classical mechanics,International Congress of Mathematicians, Amsterdam. 1954. vol 1, 315.

  • V I Arnold. Small denominators and problems of stability of motion in classical and celestial mechanics.Russ. Math. Surveys. 18.6. 85, 1963.

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  • J Moser.Stable and Random Motions in Dynamical Systems. Princeton University Press, 1973.

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  1. Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Science, 560 012, Bangalore, India

    Govindan Rangarajan

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  1. Govindan Rangarajan
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Rangarajan, G. Kolmogorov-Arnold-Moser theorem. Reson 3, 43–53 (1998). https://doi.org/10.1007/BF02834611

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  • DOI: https://doi.org/10.1007/BF02834611

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