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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

Type
Document de travail / Working paper
External document link
http://arxiv.org/abs/1005.5604v1
Date
2010
Publisher
Université Pierre et Marie Curie
Published in
Paris
Pages
19
Metadata
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Author(s)
Féjoz, Jacques
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 / Keywords
Kolmogorov's theorem