A C1 ARNOL'D-LIOUVILLE THEOREM

In this paper, we prove a version of Arnol'd-Liouville theorem for C-2 Hamiltonians having enough 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.