{
  "id": "1609.04943",
  "version": "v1",
  "published": "2016-09-16T08:21:58.000Z",
  "updated": "2016-09-16T08:21:58.000Z",
  "title": "Convergence of Dynamics and the Perron-Frobenius Operator",
  "authors": [
    "Moritz Gerlach"
  ],
  "comment": "8 pages, 0 figures",
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by a uniform mixing-like property of the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-16T08:21:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "28D05",
      "37A25",
      "47A35"
    ],
    "keywords": [
      "main result states",
      "asymptotic behavior",
      "strong convergence",
      "uniform mixing-like property",
      "associated perron-frobenius operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}