{
  "id": "1307.1983",
  "version": "v1",
  "published": "2013-07-08T08:54:55.000Z",
  "updated": "2013-07-08T08:54:55.000Z",
  "title": "On the connections between symmetries and conservation rules of dynamical systems",
  "authors": [
    "Giampaolo Cicogna"
  ],
  "comment": "13 pages, no fig",
  "journal": "Math. Meth. Appl. Sci. (ICNAAM Proc.), vol. 36 (2013)",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system can allow to obtain conserved quantities which are invariant under the symmetry. In the case of Hamiltonian dynamical systems it is shown that, if the system admits a symmetry of \"weaker\" type (specifically, a \\lambda\\ or a \\Lambda-symmetry), then the generating function of the symmetry is not a conserved quantity, but the deviation from the exact conservation is \"controlled\" in a well defined way. Several examples illustrate the various aspects.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-08T08:54:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A05",
      "37C80"
    ],
    "keywords": [
      "conservation rules",
      "conserved quantity",
      "lie point-symmetries",
      "strict connection",
      "hamiltonian dynamical systems"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1002/mma.2584",
      "journal": "Mathematical Methods in the Applied Sciences",
      "year": 2013,
      "month": "Jan",
      "volume": 36,
      "number": 2,
      "pages": 208
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013MMAS...36..208C"
    }
  }
}