{
  "id": "math/0511614",
  "version": "v1",
  "published": "2005-11-24T16:34:26.000Z",
  "updated": "2005-11-24T16:34:26.000Z",
  "title": "Exponential mixing for the Teichmuller flow",
  "authors": [
    "Artur Avila",
    "Sebastien Gouezel",
    "Jean-Christophe Yoccoz"
  ],
  "comment": "49 pages",
  "categories": [
    "math.DS",
    "math.GT"
  ],
  "abstract": "We study the dynamics of the Teichmuller flow in the moduli space of Abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Holder observables. A geometric consequence is that the $\\SL(2,\\R)$ action in the moduli space has a spectral gap.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-24T16:34:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "teichmuller flow",
      "exponential mixing",
      "moduli space",
      "absolutely continuous invariant probability measure",
      "abelian differentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11614A"
    }
  }
}