We reconsider the original proof of Kolmogorov's theorem in the light of classical perturbation methods based on expansions in some parameter. With a careful analysis of the accumulation of small divisors we prove that their effect is bounded by a geometrically increasing numerical sequence. This allows us to achieve the proof without using the so called quadratic method.
Kolmogorov theorem and classical perturbation theory / A. Giorgilli, U. Locatelli. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - 48:2(1997 Mar), pp. 220-261.
Kolmogorov theorem and classical perturbation theory
A. GiorgilliPrimo
;
1997
Abstract
We reconsider the original proof of Kolmogorov's theorem in the light of classical perturbation methods based on expansions in some parameter. With a careful analysis of the accumulation of small divisors we prove that their effect is bounded by a geometrically increasing numerical sequence. This allows us to achieve the proof without using the so called quadratic method.
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