{
  "id": "1506.02185",
  "version": "v1",
  "published": "2015-06-06T19:45:29.000Z",
  "updated": "2015-06-06T19:45:29.000Z",
  "title": "Common zeroes of families of smooth vector fields on surfaces",
  "authors": [
    "Morris W. Hirsch"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let Y and X denote C^k vector fields on a possibly noncompact surface with empty boundary, k >0. Say that Y tracks X if the dynamical system it generates locally permutes integral curves of X. Let K be a locally maximal compact set of zeroes of X. THEOREM Assume the Poincar'e-Hopf index of X at K is nonzero, and the k-jet of X at each point of K is nontrivial. If g is a supersolvable Lie algebra of C^k vector fields that track X, then the elements of g have a common zero in K. Applications are made to attractors and transformation groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-06T19:45:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H15",
      "54H25",
      "17B66"
    ],
    "keywords": [
      "smooth vector fields",
      "common zero",
      "generates locally permutes integral curves",
      "locally maximal compact set",
      "empty boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150602185H"
    }
  }
}