{
  "id": "1906.03770",
  "version": "v1",
  "published": "2019-06-10T02:29:42.000Z",
  "updated": "2019-06-10T02:29:42.000Z",
  "title": "Fixed points for branched covering maps of the plane",
  "authors": [
    "Alejo García"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "A well-known result from Brouwer states that any orientation preserving homeomorphism of the plane with no fixed points has an empty non-wandering set. In particular, an invariant compact set implies the existence of a fixed point. In this paper we give sufficient conditions for degree 2 branched covering maps of the plane to have a fixed point, namely: A totally invariant compact subset such that it does not separate the critical point from its image An invariant compact subset with a connected neighbourhood $U$, such that $\\mathrm{Fill}(U \\cup f(U))$ does not contain the critical point nor its image. An invariant continuum such that the critical point and its image belong to the same connected component of its complement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-10T02:29:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fixed point",
      "branched covering maps",
      "critical point",
      "invariant compact set implies",
      "totally invariant compact subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}