{
  "id": "math/0104215",
  "version": "v1",
  "published": "2001-04-24T14:19:38.000Z",
  "updated": "2001-04-24T14:19:38.000Z",
  "title": "A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations",
  "authors": [
    "Y. Hirata",
    "K. Imai"
  ],
  "comment": "15 pages, no figures, AMSLaTeX",
  "doi": "10.1143/JPSJ.71.2396",
  "categories": [
    "math.DS",
    "nlin.SI"
  ],
  "abstract": "Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of Lie symmetries analytic in the neighbourhood of an equilibrium point. In addition, this result can be applied to a necessary condition for existence of a Lie symmetry in quasihomogeneous systems of ordinary differential equations. With the help of our main theorem, it is proved that several systems do not possess any analytic Lie symmetries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-24T14:19:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ordinary differential equations",
      "lie symmetry",
      "necessary condition",
      "quasihomogeneous systems",
      "equilibrium point"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}