Marie-Claude Arnaud, Jinxin Xue
Published 2016-12-27Version 1
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.
Quantitative Destruction of Lagrangian Torus
A Modified Parameterization Method for Invariant Lagrangian Tori for Partially Integrable Hamiltonian Systems
Destruction of Lagrangian torus for positive definite Hamiltonian systems
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