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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Received: April 4, 1995; revised June 7, 1996
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Giorgilli, A., Locatelli, U. Kolmogorov theorem and classical perturbation theory. Z. angew. Math. Phys. 48, 220–261 (1997). https://doi.org/10.1007/PL00001475
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DOI: https://doi.org/10.1007/PL00001475