{
  "id": "1006.4086",
  "version": "v2",
  "published": "2010-06-21T14:52:16.000Z",
  "updated": "2011-03-24T13:53:41.000Z",
  "title": "The packing spectrum for Birkhoff averages on a self-affine repeller",
  "authors": [
    "Henry WJ Reeve"
  ],
  "comment": "25 pages, 2 figures; to appear in Ergodic Theory & Dynamical Systems",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the multifractal analysis for Birkhoff averages of continuous potentials on a self-affine Sierpi\\'{n}ski sponge. In particular, we give a variational principal for the packing dimension of the level sets. Furthermore, we prove that the packing spectrum is concave and continuous. We give a sufficient condition for the packing spectrum to be real analytic, but show that for general H\\\"{o}lder continuous potentials, this need not be the case. We also give a precise criterion for when the packing spectrum attains the full packing dimension of the repeller. Again, we present an example showing that this is not always the case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-24T13:53:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birkhoff averages",
      "self-affine repeller",
      "continuous potentials",
      "multifractal analysis",
      "full packing dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.4086R"
    }
  }
}