{
  "id": "1612.08755",
  "version": "v1",
  "published": "2016-12-27T21:20:48.000Z",
  "updated": "2016-12-27T21:20:48.000Z",
  "title": "A C 1 Arnol'd-Liouville Theorem",
  "authors": [
    "Marie-Claude Arnaud",
    "Jinxin Xue"
  ],
  "categories": [
    "math.DS"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-27T21:20:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arnold-liouville theorem",
      "invariant lagrangian tori",
      "lagrangian torus",
      "lipschitz regularity",
      "arnold-liouville coordinates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}