{
  "id": "0802.0520",
  "version": "v1",
  "published": "2008-02-04T21:56:53.000Z",
  "updated": "2008-02-04T21:56:53.000Z",
  "title": "Multifractal analysis of Birkhoff averages on \"self-affine\" symbolic spaces",
  "authors": [
    "Julien Barral",
    "Mounir Mensi"
  ],
  "doi": "10.1088/0951-7715/21/10/011",
  "categories": [
    "math.DS"
  ],
  "abstract": "We achieve on self-affine Sierpinski carpets the multifractal analysis of the Birkhoff averages of potentials satisfying a Dini condition. Given such a potential, the corresponding Hausdorff spectrum cannot be deduced from that of the associated Gibbs measure by a simple transformation. Indeed, these spectra are respectively obtained as the Legendre transform of two distinct concave differentiable functions that cannot be deduced from one another by a dilation and a translation. This situation is in contrast with what is observed in the familiar self-similar case. Our results are presented in the framework of almost-multiplicative functions on products of two distinct symbolic spaces and their projection on the associated self-affine carpets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-04T21:56:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78",
      "28A80",
      "37D35",
      "37D40"
    ],
    "keywords": [
      "multifractal analysis",
      "birkhoff averages",
      "self-affine sierpinski carpets",
      "distinct symbolic spaces",
      "familiar self-similar case"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Nonlinearity",
      "year": 2008,
      "month": "Oct",
      "volume": 21,
      "number": 10,
      "pages": 2409
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008Nonli..21.2409B"
    }
  }
}