%0 Journal Article %T A C1 Arnol'd-Liouville theorem %+ EA2151 Laboratoire de Mathématiques d'Avignon (LMA) %+ University of Chicago %A Arnaud, Marie-Claude %A Xue, Jinxin %Z Institut universitaire de France (M.-C. A) %Z Weak KAM beyond Hamilton-Jacobi, ANR-12-BLAN-WKBHJ (M.-C. A.) %Z NSF grant DMS-1500897 (J. X.) %< avec comité de lecture %@ 0303-1179 %J Asterisque %I Société Mathématique de France %S Quelques aspects de la théorie des systèmes dynamiques: un hommage à Jean-Christophe Yoccoz.II %V 416 %P 1-31 %8 2020 %D 2020 %Z 1612.08755 %K (C0-)Poisson commutativity %K Hamiltonian %K foliation %K Arnol'd- Liouville theorem %K Lagrangian submanifolds %K generating functions %K symplectic homeomorphisms %K complete integrability %Z 2010 Mathematics Subject Classification. 37J50, 70H20, 53D12. %Z Mathematics [math]/Dynamical Systems [math.DS] %Z Mathematics [math]/Symplectic Geometry [math.SG]Journal articles %X 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. %G English %2 https://univ-avignon.hal.science/hal-01422530v2/document %2 https://univ-avignon.hal.science/hal-01422530v2/file/C1integrablehamiltonian26juillet2017.pdf %L hal-01422530 %U https://univ-avignon.hal.science/hal-01422530 %~ UNIV-AVIGNON %~ INSMI %~ TDS-MACS %~ LMA-UAPV %~ ANR