A C1 Arnol'd-Liouville theorem
Dynamical Systems
2017-08-17 v2
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.
Cite
@article{arxiv.1612.08755,
title = {A C1 Arnol'd-Liouville theorem},
author = {Marie-Claude Arnaud and Jinxin Xue},
journal= {arXiv preprint arXiv:1612.08755},
year = {2017}
}