A C1 Arnol'd-Liouville theorem - Archive ouverte HAL Access content directly
Journal Articles Asterisque Year : 2020

A C1 Arnol'd-Liouville theorem

(1) , (2)
1
2

Abstract

In this paper, we prove a version of Arnol'd-Liouville theorem for C 1 commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori is crucial to determine the Dynamics on each Lagrangian torus and that the C 1 regularity of the foliation by invariant Lagrangian tori is crucial to prove the continuity of Arnol'd-Liouville coordinates. We also explore various notions of C 0 and Lipschitz integrability.
Fichier principal
Vignette du fichier
C1integrablehamiltonian26juillet2017.pdf (334.3 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01422530 , version 1 (26-12-2016)
hal-01422530 , version 2 (16-08-2017)

Identifiers

Cite

Marie-Claude Arnaud, Jinxin Xue. A C1 Arnol'd-Liouville theorem. Asterisque, 2020, Quelques aspects de la théorie des systèmes dynamiques: un hommage à Jean-Christophe Yoccoz.II, 416, pp.1-31. ⟨hal-01422530v2⟩
480 View
521 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More