{
  "id": "0809.1074",
  "version": "v3",
  "published": "2008-09-05T16:56:02.000Z",
  "updated": "2009-11-16T20:06:18.000Z",
  "title": "Multifractal analysis for multimodal maps",
  "authors": [
    "Mike Todd"
  ],
  "comment": "Minor rewrites",
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a multimodal interval map $f:I \\to I$ and a H\\\"older potential $\\phi:I \\to \\mathbb{R}$, we study the dimension spectrum for equilibrium states of $\\phi$. The main tool here is inducing schemes, used to overcome the presence of critical points. The key issue is to show that enough points are `seen' by a class of inducing schemes. We also compute the Lyapunov spectrum. We obtain the strongest results when $f$ is a Collet-Eckmann map, but our analysis also holds for maps satisfying much weaker growth conditions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-11-16T20:06:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "37D25",
      "37D35",
      "37C45"
    ],
    "keywords": [
      "multimodal maps",
      "multifractal analysis",
      "multimodal interval map",
      "inducing schemes",
      "weaker growth conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.1074T"
    }
  }
}