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A C 1 ARNOL'D-LIOUVILLE THEOREM

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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Dates and versions

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

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Marie-Claude Arnaud, Jinxin Xue. A C 1 ARNOL'D-LIOUVILLE THEOREM. 2016. ⟨hal-01422530v1⟩
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