{
  "id": "1311.4083",
  "version": "v1",
  "published": "2013-11-16T17:53:38.000Z",
  "updated": "2013-11-16T17:53:38.000Z",
  "title": "Inheriting of chaos in nonautonomous dynamical systems",
  "authors": [
    "Marta Štefánková"
  ],
  "comment": "6 pages, no figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider nonautonomous discrete dynamical systems $\\{ f_n\\}_{n\\ge 1}$, where every $f_n$ is a surjective continuous map $[0,1]\\to [0,1]$ such that $f_n$ converges uniformly to a map $f$. We show, among others, that if $f$ is chaotic in the sense of Li and Yorke then the nonautonomous system $ \\{ f_n\\}_{n\\ge 1}$ is Li-Yorke chaotic as well, and that the same is true for distributional chaos. If $f$ has zero topological entropy then the nonautonomous system inherits its infinite $\\omega$-limit sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-16T17:53:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37B20",
      "37B40",
      "37B55",
      "54H20"
    ],
    "keywords": [
      "nonautonomous dynamical systems",
      "inheriting",
      "nonautonomous discrete dynamical systems",
      "li-yorke chaotic",
      "distributional chaos"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.4083S"
    }
  }
}