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.}
Giorgilli, A., Locatelli, U. (1997). Kolmogorov theorem and classical perturbation theory. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 48, 220-261 [10.1007/PL00001475].
Kolmogorov theorem and classical perturbation theory
LOCATELLI, UGO
1997-01-01
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.}File in questo prodotto:
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