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Zbl 0836.34040
Chierchia, L.; Falcolini, C.
A direct proof of a theorem by Kolmogorov in Hamiltonian systems. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 21, No.4, 541-593 (1994). ISSN 0391-173X

The authors prove Kolmogorov's theorem on the existence of quasi-periodic solutions of nearly integrable Hamiltonian systems by means of Siegel's method. They refer to {\it L. H. Eliasson}'s paper [Reports Department of Math., Univ. of Stockholm, Sweden, No. 2, 1-31 (1988)] where such a proof has been published for the first time. In the author's opinion their proof is simpler, at least from a conceptual -- if not from a technical - - point of view, than the proof of Eliasson.
[H.Rüssmann (Mainz)]

MSC 2000:: *34C27 Almost periodic solutions of ODE
34D05 Asymptotic stability of ODE
34A25 Analytical theory of ODE
37J99 Finite-dimensional Hamiltonian etc. systems

Keywords: Kolmogorov's theorem; quasi-periodic solutions; nearly integrable; Hamiltonian systems; Siegel's method

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