Regular and Chaotic Dynamics

, Volume 13, Issue 2, pp 130–139 | Cite as

Kolmogorov’s 1954 paper on nearly-integrable Hamiltonian systems

Review Articles

Abstract

Following closely Kolmogorov’s original paper [1], we give a complete proof of his celebrated Theorem on perturbations of integrable Hamiltonian systems by including few “straightforward” estimates.

Key words

Kolmogorov’s theorem KAM theory small divisors Hamiltonian systems perturbation theory symplectic transformations nearly-integrable systems 

MSC2000 numbers

37J40 70H08 37J05 37J25 

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References

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    Kolmogorov, A.N., On the Conservation of Conditionally Periodic Motions under Small Perturbation of the Hamiltonian, Dokl. akad. nauk SSSR, 1954, vol. 98, pp. 527–530. Engl. transl.: Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Volta Memorial conference, Como, 1977, Lecture Notes in Physics, vol. 93, Springer, 1979, pp. 51–56.MATHMathSciNetGoogle Scholar
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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità “Roma Tre”RomaItaly

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