{
  "id": "math/0108064",
  "version": "v2",
  "published": "2001-08-08T15:50:53.000Z",
  "updated": "2002-09-23T18:15:10.000Z",
  "title": "A fixed point theorem for bounded dynamical systems",
  "authors": [
    "David Richeson",
    "Jim Wiseman"
  ],
  "comment": "4 pages, minor clarifications",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that a continuous map or a continuous flow on $\\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\\R^{n}$ intersects W then there is a fixed point in W. Consequently, if the omega limit set of every point is nonempty and uniformly bounded then there is a fixed point.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-09-23T18:15:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54H25",
      "37B30",
      "37B25"
    ],
    "keywords": [
      "fixed point theorem",
      "bounded dynamical systems",
      "omega limit set",
      "recurrence relation",
      "compact set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......8064R"
    }
  }
}