{
  "id": "1512.06940",
  "version": "v1",
  "published": "2015-12-22T03:06:29.000Z",
  "updated": "2015-12-22T03:06:29.000Z",
  "title": "Induced Dynamics on the Hyperspaces",
  "authors": [
    "Puneet Sharma"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we study the dynamics induced by finite commutative relation on the hyperspaces. We prove that the dynamics induced on the hyperspace by a non-trivial commutative family of continuous self maps cannot be transitive and hence cannot exhibit higher degrees of mixing. We also prove that the dynamics induced on the hyperspace by such a collection cannot have dense set of periodic points. We also give example to show that the induced dynamics in this case may or may not be sensitive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-22T03:06:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B20",
      "37B99",
      "54C60",
      "54H20"
    ],
    "keywords": [
      "induced dynamics",
      "hyperspace",
      "dense set",
      "higher degrees",
      "finite commutative relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151206940S"
    }
  }
}