{
  "id": "0903.0503",
  "version": "v2",
  "published": "2009-03-03T11:43:40.000Z",
  "updated": "2009-03-08T06:39:27.000Z",
  "title": "Approximate transitivity property and Lebesgue spectrum",
  "authors": [
    "El Houcein El Abdalaoui",
    "Mariusz Lemanczyk"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Exploiting a spectral criterion for a system not to be AT we give some new examples of zero entropy systems without the AT property. Our examples include those with finite spectral multiplicity -- in particular we show that the system arising from the Rudin-Shapiro substitution is not AT. We also show that some nil-rotations on a quotient of the Heisenberg group as well as some (generalized) Gaussian systems are not AT. All known examples of non AT-automorphisms contain a Lebesgue component in the spectrum.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-08T06:39:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A15",
      "37A25"
    ],
    "keywords": [
      "approximate transitivity property",
      "lebesgue spectrum",
      "finite spectral multiplicity",
      "zero entropy systems",
      "non at-automorphisms contain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.0503H"
    }
  }
}