{
  "id": "math/0604035",
  "version": "v1",
  "published": "2006-04-03T13:19:46.000Z",
  "updated": "2006-04-03T13:19:46.000Z",
  "title": "Phase transitions for the multifractal analysis of self-similar measures",
  "authors": [
    "Benoit Testud"
  ],
  "comment": "Article accept\\'{e} pour publication dans Nonlinearity. Article en ligne \\`{a} http://www.iop.org/EJ/journal/Non",
  "doi": "10.1088/0951-7715/19/5/009",
  "categories": [
    "math.CA"
  ],
  "abstract": "We study the multifractal analysis of a class of self-similar measures with overlaps. This class, for which we obtain explicit formulae for the L^q spectrum tau(q) as well as the singularity spectrum f(alpha), is sufficiently large to point out new phenomena concerning the multifractal structure of self-similar measures. We show, that unlike the classical quasi-Bernoulli case, the L^q spectrum can have an arbitrarely large number of non-differentiability points (phase transitions). These singularities occur only for the negative values of q and yield to measures that do not satisfy the multifractal formalism. The weak quasi-Bernoulli property is the key point of most of the arguments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-03T13:19:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "28A78"
    ],
    "keywords": [
      "self-similar measures",
      "multifractal analysis",
      "phase transitions",
      "weak quasi-bernoulli property",
      "singularity spectrum"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}