Ontology type: schema:Chapter
1999
AUTHORS ABSTRACTThe celebrated theorem of Kolmogorov on persistence of invariant tori of a nearly integrable Hamiltonian system is revisited in the light of classical perturbation algorithm. It is shown that the original Kolmogorov’s algorithm can be given the form of a constructive scheme based on expansion in a parameter. A careful analysis of the accumulation of the small divisors shows that it can be controlled geometrically. As a consequence, the proof of convergence is based essentially on Cauchy’s majorants method, with no use of the so called quadratic method. A short comparison with Lindstedt’s series is included. More... »
PAGES72-89
Hamiltonian Systems with Three or More Degrees of Freedom
ISBN
978-94-010-5968-8
978-94-011-4673-9
http://scigraph.springernature.com/pub.10.1007/978-94-011-4673-9_8
DOIhttp://dx.doi.org/10.1007/978-94-011-4673-9_8
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