{
  "id": "1211.0105",
  "version": "v2",
  "published": "2012-11-01T06:47:48.000Z",
  "updated": "2013-02-26T12:34:56.000Z",
  "title": "Hypercyclic operators, Gauss measures and Polish dynamical systems",
  "authors": [
    "Iftah Dayan",
    "Eli Glasner"
  ],
  "comment": "The new version corrects the statement and proof of Theorem 1.7",
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "In this work we consider hypercyclic operators as a special case of Polish dynamical systems. In the first section we analyze the construction of Bayart and Grivaux of a hypercyclic operator which preserves a Gaussian measure, and derive a description of the maximal spectral type of the Koopman operator associated to the corresponding measure preserving dynamical system. We then use this information to show the existence of a mildly but not strongly mixing hypercyclic operator on Hilbert space. In the last two sections we study hypercyclic and frequently hypecyclic operators which, as Polish dynamical systems are, M-systems, E-systems, and syndetically transitive systems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-02-26T12:34:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polish dynamical systems",
      "hypercyclic operator",
      "gauss measures",
      "maximal spectral type",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.0105D"
    }
  }
}