{
  "id": "1203.5455",
  "version": "v2",
  "published": "2012-03-24T22:37:07.000Z",
  "updated": "2012-06-10T20:51:13.000Z",
  "title": "The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows",
  "authors": [
    "Elena A. Kudryavtseva"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DG",
    "math.CV",
    "math.DS",
    "math.SG"
  ],
  "abstract": "For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an \"exact\" 2-parameter family of flat polygons equipped with certain pairing of sides. For the integrable Hamiltonian systems given by the vector field $v=(-\\partial f/\\partial w, \\partial f/\\partial z)$ on ${\\mathbb C}^2$ where $f=f(z,w)$ is a complex polynomial in 2 variables, geometric properties of Liouville fibrations are described.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-10T20:51:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J05",
      "37J35"
    ],
    "keywords": [
      "integrable hamiltonian systems",
      "incomplete flows",
      "liouville-type theorem",
      "hamiltonian vector fields",
      "liouville theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.5455K"
    }
  }
}