{
  "id": "math/0010197",
  "version": "v1",
  "published": "2000-10-20T09:32:13.000Z",
  "updated": "2000-10-20T09:32:13.000Z",
  "title": "On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations",
  "authors": [
    "Alexei Tsygvintsev"
  ],
  "comment": "9 pages. to appear in . Phys. A: Math. Gen. 33, 2000",
  "doi": "10.1088/0305-4470/34/11/311",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider systems of ordinary differential equations with quadratic homogeneous right hand side. We give a new simple proof of a result already obtained in [8,10] which gives the necessary conditions for the existence of polynomial first integrals. The necessary conditions for the existence of a polynomial symmetry field are given. It is proved that an arbitrary homogeneous first integral of a given degree is a linear combination of a fixed set of polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-10-20T09:32:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37K10"
    ],
    "keywords": [
      "ordinary differential equations",
      "polynomial first integrals",
      "quadratic homogeneous systems",
      "quadratic homogeneous right hand side",
      "necessary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}