{
  "id": "1110.2365",
  "version": "v2",
  "published": "2011-10-11T13:19:14.000Z",
  "updated": "2011-10-14T12:36:06.000Z",
  "title": "Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows",
  "authors": [
    "Artur Avila",
    "Marcelo Viana",
    "Amie Wilkinson"
  ],
  "comment": "29 pages. Small error in statement of Theorem A corrected from previous version (\"k points\" replaced by \"k orbits\")",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider volume-preserving perturbations of the time-one map of the geodesic flow of a compact surface with negative curvature. We show that if the Liouville measure has Lebesgue disintegration along the center foliation then the perturbation is itself the time-one map of a smooth volume-preserving flow, and that otherwise the disintegration is necessarily atomic.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-14T12:36:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C40",
      "37C85"
    ],
    "keywords": [
      "geodesic flow",
      "lyapunov exponents",
      "absolute continuity",
      "time-one map",
      "compact surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.2365A"
    }
  }
}