{
  "id": "1410.5857",
  "version": "v1",
  "published": "2014-10-21T21:11:21.000Z",
  "updated": "2014-10-21T21:11:21.000Z",
  "title": "Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits",
  "authors": [
    "T. C. Batista",
    "J. S. Gonschorowski",
    "F. A. Tal"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $K$ be the Cantor set. We prove that arbitrarily close to a homeomorphism $T:K\\rightarrow K$ there exists a homeomorphism $\\widetilde T:K\\rightarrow K$ such that the $\\alpha$-limit and the $\\omega$-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism $T:K\\rightarrow K$ there exists an endomorphism $\\widetilde T:K\\rightarrow K$ close to $T$ such that every orbit is finally periodic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-21T21:11:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ergodic measures",
      "periodic orbit",
      "symbolic dynamics",
      "arbitrarily close",
      "cantor set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.5857B"
    }
  }
}