A C1 Arnol'd-Liouville theorem

Marie-Claude Arnaud; Jinxin Xue

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arXiv · 1612.08755

A C1 Arnol'd-Liouville theorem

Marie-Claude Arnaud·Jinxin Xue

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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.

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Marie-Claude Arnaud, Jinxin Xue. 2016-12-27. A C1 Arnol'd-Liouville theorem. https://arxiv.org/abs/1612.08755

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