{
  "id": "1203.5170",
  "version": "v2",
  "published": "2012-03-23T03:27:28.000Z",
  "updated": "2012-04-24T22:16:13.000Z",
  "title": "Genericity of non-uniform hyperbolicity in dimension 3",
  "authors": [
    "Jana Rodriguez Hertz"
  ],
  "comment": "to appear in Journal of Modern Dynamics",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a generic conservative diffeomorphism of a 3-manifold M, the Oseledets splitting is a globally dominated splitting. Moreover, either all Lyapunov exponents vanish almost everywhere, or else the system is non-uniformly hyperbolic and ergodic. This is the 3-dimensional version of a well-known result by Ma\\~n\\'e-Bochi, stating that a generic conservative surface diffeomorphism is either Anosov or all Lyapunov exponents vanish almost everywhere. This result inspired and answers in the positive for dimension 3 a conjecture by Avila and Bochi. We also prove that all partially hyperbolic sets with positive measure and center dimension one have a strong homoclinic intersection. This implies that Cr generically for any r, a diffeomorphism contains no proper partially hyperbolic sets with positive measure and center dimension one.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-24T22:16:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37C20"
    ],
    "keywords": [
      "non-uniform hyperbolicity",
      "genericity",
      "center dimension",
      "lyapunov exponents vanish",
      "proper partially hyperbolic sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.5170R"
    }
  }
}