KOLMOGOROV THEOREM AND CLASSICAL PERTURBATION-THEORY

Authors
GIORGILLI A LOCATELLI U
Citation
A. Giorgilli et U. Locatelli, KOLMOGOROV THEOREM AND CLASSICAL PERTURBATION-THEORY, Zeitschrift fur angewandte Mathematik und Physik, 48(2), 1997, pp. 220-261
Citations number
21
Categorie Soggetti
Mathematics,"Mathematical Method, Physical Science",Mathematics
Journal title
Zeitschrift fur angewandte Mathematik und Physik → ACNP
ISSN journal
00442275
Volume
48
Issue
2
Year of publication
1997
Pages
220 - 261
Database
ISI
SICI code
0044-2275(1997)48:2<220:KTACP>2.0.ZU;2-H
Abstract
We reconsider the original proof of Kolmogorov's theorem in the light of classical perturbation methods based on expansions in some paramete r. With a careful analysis of the accumulation of small divisors we pr ove that their effect is bounded by a geometrically increasing numeric al sequence. This allows us to achieve the proof without using the so called quadratic method.