{
  "id": "1611.08994",
  "version": "v1",
  "published": "2016-11-28T06:04:34.000Z",
  "updated": "2016-11-28T06:04:34.000Z",
  "title": "Topological stability and pseudo-orbit tracing property of group actions",
  "authors": [
    "Nhan-Phu Chung",
    "Keonhee Lee"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this note we extend the concept of topological stability from homeomorphisms to group actions on compact metric spaces, and prove that if an action of a finitely generated group is expansive and has the pseudo-orbit tracing property then it is topologically stable. This represents a group action version of the Walter's stability theorem. Moreover we give a class of group actions with topological stability or pseudo-orbit tracing property. On the other hand, we also provide a characterization of subshifts of finite type over finitely generated groups in term of pseudo-orbit tracing property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-28T06:04:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pseudo-orbit tracing property",
      "topological stability",
      "finitely generated group",
      "group action version",
      "compact metric spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}