A simple proof of the invariant torus theorem
Féjoz, Jacques (2010), A simple proof of the invariant torus theorem. https://basepub.dauphine.fr/handle/123456789/7480
TypeDocument de travail / Working paper
External document linkhttp://arxiv.org/abs/1005.5604v1
Université Pierre et Marie Curie
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Abstract (EN)We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency obstruction from one side of the conjugacy to another. Then the proof consists in applying a simple, well suited, inverse function theorem in the analytic category, which itself relies on the Newton algorithm and on interpolation inequalities. A comparison with other proofs is included in appendix.
Subjects / KeywordsKolmogorov's theorem
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