{
  "id": "2008.05795",
  "version": "v1",
  "published": "2020-08-13T10:16:09.000Z",
  "updated": "2020-08-13T10:16:09.000Z",
  "title": "Topologically stable and $β$-persistent points of group actions",
  "authors": [
    "Abdul Gaffar Khan",
    "Tarun Das"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we introduce topologically stable points and $\\beta$-persistent points for finitely generated group actions on compact metric spaces. We prove that every shadowable point of an expansive action on a compact metric space is a topologically stable point. We justify that the expansivity of an action is not a necessary condition for the topological stability of a shadowable point of that action and the existence of a dense set of topologically stable points need not imply the topological stability of that action. Finally, we prove that every equicontinuous pointwise topologically stable action on a compact metric space is $\\beta$-persistent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-13T10:16:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C85",
      "37B25",
      "37B05"
    ],
    "keywords": [
      "persistent points",
      "compact metric space",
      "topologically stable point",
      "pointwise topologically stable action",
      "topological stability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}