A simple proof of the invariant torus theorem

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 anothe...

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Bibliographic Details
Published in:Regular & chaotic dynamics 2012, Vol.17 (1), p.1-5
Main Author: Fejoz, Jacques
Format: Article
Language:English
Subjects:
Dynamical Systems
Mathematics
Online Access:Get full text
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Summary: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.
ISSN:1560-3547
1468-4845