Positive measure of KAM tori for finitely differentiable Hamiltonians - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal de l'École polytechnique — Mathématiques Année : 2020

Positive measure of KAM tori for finitely differentiable Hamiltonians

Résumé

Consider an integer $n \geq 2$ and real numbers $\tau>n-1$ and $l>2(\tau+1)$. Using ideas of Moser, Salamon proved that individual Diophantine tori persist for Hamiltonian systems which are of class $C^l$. Under the stronger assumption that the system is a $C^{l+\tau}$ perturbation of an analytic integrable system, P{\"o}schel proved the persistence of a set of positive measure of Diophantine tori. We improve the last result by showing it is sufficient for the perturbation to be of class $C^{l}$ and the integrable part to be of class $C^{l+2}$.
Fichier principal
Vignette du fichier
KAMmesCl.pdf (178.5 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01947601 , version 1 (07-12-2018)
hal-01947601 , version 2 (13-12-2018)

Identifiants

Citer

Abed Bounemoura. Positive measure of KAM tori for finitely differentiable Hamiltonians. Journal de l'École polytechnique — Mathématiques, 2020, Tome 7. ⟨hal-01947601v2⟩
55 Consultations
76 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More