{
  "id": "1203.1663",
  "version": "v1",
  "published": "2012-03-08T00:08:57.000Z",
  "updated": "2012-03-08T00:08:57.000Z",
  "title": "The Geometry of Integrable and Superintegrable Systems",
  "authors": [
    "A. Ibort",
    "G. Marmo"
  ],
  "categories": [
    "math-ph",
    "math.DS",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical structure like symplectic, Poisson, etc. Such geometrical structure provides a generalized toroidal bundle on the carrier space of the system. Non--canonical diffeomorphisms of such structure generate alternative Hamiltonian structures for complete integrable Hamiltonian systems. The energy-period theorem provides the first non--trivial obstruction for the equivalence of integrable systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-08T00:08:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70H06",
      "37J35"
    ],
    "keywords": [
      "superintegrable systems",
      "structure generate alternative hamiltonian structures",
      "normal form representation",
      "complete integrable hamiltonian systems",
      "first non-trivial obstruction"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s11232-012-0099-1",
      "journal": "Theoretical and Mathematical Physics",
      "year": 2012,
      "month": "Aug",
      "volume": 172,
      "number": 2,
      "pages": 1109
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1093497,
      "adsabs": "2012TMP...172.1109I"
    }
  }
}