Article Dans Une Revue Regular and Chaotic Dynamics Année : 2012

A simple proof of the invariant torus theorem

Résumé

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.

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Dates et versions

hal-00474037 , version 1 (18-04-2010)
hal-00474037 , version 2 (14-05-2010)

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Jacques Fejoz. A simple proof of the invariant torus theorem. Regular and Chaotic Dynamics, 2012, 17 (1), pp.1-5. ⟨hal-00474037v2⟩
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