{
  "id": "0803.1522",
  "version": "v1",
  "published": "2008-03-11T05:27:56.000Z",
  "updated": "2008-03-11T05:27:56.000Z",
  "title": "Birkhoff spectra for one-dimensional maps with some hyperbolicity",
  "authors": [
    "Yong Moo Chung"
  ],
  "comment": "21 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the multifractal analysis for smooth dynamical systems in dimension one. It is characterized the Hausdorff dimension of the level set obtained from the Birkhoff averages of a continuous function by the local dimensions of hyperbolic measures for a topologically mixing $C^2$ map modelled by an abstract dynamical system. A characterization which corresponds to above is also given for the ergodic basins of invariant probability measures. And it is shown that the complement of the set of quasi-regular points carries full Hausdorff dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-11T05:27:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45"
    ],
    "keywords": [
      "one-dimensional maps",
      "birkhoff spectra",
      "quasi-regular points carries full hausdorff",
      "points carries full hausdorff dimension",
      "hyperbolicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1522M"
    }
  }
}