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A C1 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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https://hal-univ-avignon.archives-ouvertes.fr/hal-01422530
Contributor : Marie-Claude Arnaud Connect in order to contact the contributor
Submitted on : Wednesday, August 16, 2017 - 3:18:29 PM
Last modification on : Tuesday, February 22, 2022 - 11:36:04 AM

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  • HAL Id : hal-01422530, version 2
  • ARXIV : 1612.08755

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

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