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A direct proof of a theorem by Kolmogorov in Hamiltonian systems. (English) Zbl 0836.34040

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 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.

MSC:

34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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References:

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