{
  "id": "math/0009020",
  "version": "v1",
  "published": "2000-09-02T03:28:07.000Z",
  "updated": "2000-09-02T03:28:07.000Z",
  "title": "Multiplicity of Invariant Algebraic Curves and Darboux Integrability",
  "authors": [
    "Jaume Llibre",
    "Jorge Vitorio Pereira"
  ],
  "comment": "16 pages, LaTeX",
  "categories": [
    "math.DS"
  ],
  "abstract": "We define four different kinds of multiplicity of an invariant algebraic curve for a given polynomial vector field and investigate their relationships. After taking a closer look at the singularities and at the line of infinity, we improve the Darboux theory of integrability using these new notions of multiplicity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-09-02T03:28:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "invariant algebraic curve",
      "darboux integrability",
      "multiplicity",
      "polynomial vector field",
      "closer look"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......9020L"
    }
  }
}