{
  "id": "math/0106013",
  "version": "v1",
  "published": "2001-06-04T21:06:15.000Z",
  "updated": "2001-06-04T21:06:15.000Z",
  "title": "Symplectic topology of integrable Hamiltonian systems, I: Arnold-Liouville with singularities",
  "authors": [
    "Nguyen Tien Zung"
  ],
  "comment": "Old paper put here for archival purposes. Contains a list of errata. 32 pages (=37 pages in Compositio), 1 figure",
  "journal": "Compositio Mathematica 101 (1996), 179-215",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The classical Arnold-Liouville theorem describes the geometry of an integrable Hamiltonian system near a regular level set of the moment map. Our results describe it near a nondegenerate singular level set: a tubular neighborhood of a connected singular nondegenerate level set, after a normal finite covering, admits a non-complete system of action-angle functions (the number of action functions is equal to the rank of the moment map), and it can be decomposed topologically, together with the associated singular Lagrangian foliation, to a direct product of simplest (codimension 1 and codimension 2) singularities. These results are essential for the global topological study of integrable Hamiltonian systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-06-04T21:06:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58F07",
      "58F14",
      "58F05",
      "70H05"
    ],
    "keywords": [
      "integrable hamiltonian system",
      "symplectic topology",
      "singularities",
      "arnold-liouville",
      "connected singular nondegenerate level set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......6013T"
    }
  }
}