{
  "id": "2011.13975",
  "version": "v1",
  "published": "2020-11-27T19:43:41.000Z",
  "updated": "2020-11-27T19:43:41.000Z",
  "title": "On definition of Devaney chaos for a continuous group action on a Hausdorff uniform space",
  "authors": [
    "Barbora Volna"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.DS",
    "math.GN"
  ],
  "abstract": "We show that the existence of a dense set of periodic points for a topologically transitive non-minimal continuous group action on a Hausdorff uniform space with an infinite acting group does not necessarily imply a sensitive dependence to the initial conditions in such a system. This leads to define the chaos in the sense of Devaney for a continuous group action on a Hausdorff uniform spaces with an infinite acting group in the original way, i.e. a non-minimal topologically transitive and sensitive system with a dense set of periodic points is a chaotic system in the sense of Devaney.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-27T19:43:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "54H11",
      "37D45",
      "34A60"
    ],
    "keywords": [
      "hausdorff uniform space",
      "devaney chaos",
      "non-minimal continuous group action",
      "transitive non-minimal continuous group",
      "infinite acting group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}