{
  "id": "1905.01404",
  "version": "v1",
  "published": "2019-05-04T01:21:35.000Z",
  "updated": "2019-05-04T01:21:35.000Z",
  "title": "Dynamics on the Morse Boundary",
  "authors": [
    "Qing Liu"
  ],
  "comment": "18 pages, 4 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "Let $X$ be a proper geodesic metric space and let $G$ be a group of isometries of $X$ which acts geometrically. Cordes constructed the Morse boundary of $X$ which generalizes the contracting boundary for CAT(0) spaces and the visual boundary for hyperbolic spaces. We characterize Morse elements in $G$ by their fixed points on the Morse boundary $\\partial_MX$. The dynamics on the Morse boundary is very similar to that of a $\\delta$-hyperbolic space. In particular, we show that the action of $G$ on $\\partial_MX$ is minimal if $G$ is not virtually cyclic. We also get a uniform convergence result on the Morse boundary which gives us a weak north-south dynamics for a Morse isometry. This generalizes the work of Murray in the case of the contracting boundary of a CAT(0) space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-04T01:21:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "morse boundary",
      "proper geodesic metric space",
      "hyperbolic space",
      "weak north-south dynamics",
      "contracting boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}