Name: A C^1 Arnol'd-Liouville theorem
Keywords: [MATH.MATH-SG] Mathematics [math]/Symplectic Geometry [math.SG], foliation, (C0-)Poisson commutativity, Arnol'd- Liouville theorem, generating functions, FOS: Mathematics, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], complete integrability, symplectic homeomorphisms, Dynamical Systems (math.DS)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2020Embargo end date: 01 Jan 2016Publisher:Societe Mathematique de FranceJournal:Astérisque, volume 416, pages 1-31 (issn: 0303-1179, eissn: 2492-5926,

Authors: Marie-Claude Arnaud; Jinxin Xue;

doi: 10.24033/ast.1109 , 10.24033/ast.11109 , 10.48550/arxiv.1612.08755

arXiv: http://arxiv.org/abs/1612.08755

A C^1 Arnol'd-Liouville theorem

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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.

Related Organizations

University of Chicago
United States
University of Avignon
France

Keywords

[MATH.MATH-SG] Mathematics [math]/Symplectic Geometry [math.SG], foliation, (C0-)Poisson commutativity, Arnol'd- Liouville theorem, generating functions, FOS: Mathematics, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], complete integrability, symplectic homeomorphisms, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Lagrangian submanifolds, Hamiltonian

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