A simple proof of the invariant torus theorem - Archive ouverte HAL Accéder directement au contenu
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.
Fichier principal
Vignette du fichier
simpleKam.pdf (222.91 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

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

Identifiants

Citer

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

Altmetric

Partager

Gmail Facebook X LinkedIn More