{
  "id": "1302.4091",
  "version": "v2",
  "published": "2013-02-17T17:14:01.000Z",
  "updated": "2013-06-29T15:30:51.000Z",
  "title": "SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular",
  "authors": [
    "Artur Avila",
    "Carlos Matheus",
    "Jean-Christophe Yoccoz"
  ],
  "comment": "Final version based on the referee's report. To appear in GAFA",
  "journal": "GAFA 23 (2013), 1705-1729",
  "categories": [
    "math.DS"
  ],
  "abstract": "In the moduli space $H_g$ of normalized translation surfaces of genus $g$, consider, for a small parameter $\\rho >0$, those translation surfaces which have two non-parallel saddle-connections of length $\\leq \\rho$. We prove that this subset of $H_g$ has measure $o(\\rho^2)$ w.r.t. any probability measure on $H_g$ which is invariant under the natural action of $SL(2,R)$. This implies that any such probability measure is regular, a property which is important in relation with the recent fundamental work of Eskin-Kontsevich-Zorich on the Lyapunov exponents of the KZ-cocycle.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-29T15:30:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measure",
      "moduli space",
      "lyapunov exponents",
      "small parameter",
      "non-parallel saddle-connections"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.4091A"
    }
  }
}