{
  "id": "1405.2541",
  "version": "v3",
  "published": "2014-05-11T15:46:38.000Z",
  "updated": "2015-04-21T14:16:33.000Z",
  "title": "Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets",
  "authors": [
    "Thiago Bomfim",
    "Paulo Varandas"
  ],
  "comment": "23 pages, 3 figures. Revised version according to the referee suggestions; to appear in Ergod. Th. & Dynam. Sys",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this article we prove estimates for the topological pressure of the set of points whose Birkhoff time averages are far from the space averages corresponding to the unique equilibrium state that has a weak Gibbs property. In particular, if $f$ has an expanding repeller and $\\phi$ is an H\\\"older continuous potential we prove that the topological pressure of the set of points whose accumulation values of Birkhoff averages belong to some interval $I\\subset \\mathbb R$ can be expressed in terms of the topological pressure of the whole system and the large deviations rate function. As a byproduct we deduce that most irregular sets for maps with the specification property have topological pressure strictly smaller than the whole system. Some extensions to a non-uniformly hyperbolic setting, level-2 irregular sets and hyperbolic flows are also given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-27T00:48:33.000Z",
      "title": "Multifractal analysis of irregular sets for weak Gibbs measures",
      "comment": "26 pages, 3 figures. Comments are welcome. Several typos were corrected, references and a new example was included",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-21T14:16:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "37D20",
      "60F10",
      "37D25",
      "37C30"
    ],
    "keywords": [
      "weak gibbs measures",
      "irregular sets",
      "multifractal analysis",
      "topological pressure",
      "large deviations rate function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2541B"
    }
  }
}