{
  "id": "2005.13940",
  "version": "v1",
  "published": "2020-05-28T12:15:08.000Z",
  "updated": "2020-05-28T12:15:08.000Z",
  "title": "Uniformly Positive Entropy of Induced Transformations",
  "authors": [
    "Nilson C. Bernardes Jr.",
    "Udayan B. Darji",
    "Rômulo M. Vermersch"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $(X,T)$ be a topological dynamical system consisting of a compact metric space $X$ and a continuous surjective map $T : X \\to X$. By using local entropy theory, we prove that $(X,T)$ has uniformly positive entropy if and only if so does the induced system $(\\cM(X),\\wt{T})$ on the space of Borel probability measures endowed with the weak$^*$ topology. This result can be seen as a version for the notion of uniformly positive entropy of the corresponding result for topological entropy due to Glasner and Weiss.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-28T12:15:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B40",
      "28A33",
      "60B10",
      "54B20"
    ],
    "keywords": [
      "uniformly positive entropy",
      "induced transformations",
      "borel probability measures",
      "compact metric space",
      "local entropy theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}