{
  "id": "1304.2447",
  "version": "v1",
  "published": "2013-04-09T02:20:56.000Z",
  "updated": "2013-04-09T02:20:56.000Z",
  "title": "Equivalent conditions of Devaney chaos on the hyperspace",
  "authors": [
    "Jian Li"
  ],
  "comment": "5 pages",
  "journal": "J. Univ. Sci. Technol. China, 44, 2014, no.2, 93-95",
  "doi": "10.3969/j.issn.0253-2778.2014.02.002",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $T$ be a continuous self-map of a compact metric space $X$. The transformation $T$ induces natural a continuous self-map $T_K$ on the hyperspace $K(X)$ of all non-empty closed subsets of $X$. In this paper, we show that the system $(K(X),T_K)$ on the hyperspace is Devaney chaotic if and only if $(K(X),T_K)$ is an HY-system if and only if $(X,T)$ is an HY-system, where a system $(Y,S)$ is called an HY-system if it is totally transitive and has dense small periodic sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-09T02:20:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B99",
      "54H20",
      "54B20"
    ],
    "keywords": [
      "devaney chaos",
      "equivalent conditions",
      "hyperspace",
      "dense small periodic sets",
      "continuous self-map"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.2447L"
    }
  }
}