{
  "id": "0710.2353",
  "version": "v1",
  "published": "2007-10-11T21:47:38.000Z",
  "updated": "2007-10-11T21:47:38.000Z",
  "title": "A Criterion For Ergodicity of Non-uniformly hyperbolic Diffeomorphisms",
  "authors": [
    "F. Rodriguez Hertz",
    "M. A. Rodriguez Hertz",
    "A. Tahzibi",
    "R. Ures"
  ],
  "comment": "A Research Announcement",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this work we exhibit a new criteria for ergodicity of diffeomorphisms involving conditions on Lyapunov exponents and general position of some invariant manifolds. On one hand we derive uniqueness of SRB-measures for transitive surface diffeomorphisms. On the other hand, using recent results on the existence of blenders we give a positive answer, in the $C^1$ topology, to a conjecture of Pugh-Shub in the context of partially hyperbolic conservative diffeomorphisms with two dimensional center bundle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-11T21:47:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D30",
      "37D35"
    ],
    "keywords": [
      "non-uniformly hyperbolic diffeomorphisms",
      "ergodicity",
      "dimensional center bundle",
      "general position",
      "transitive surface diffeomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.2353R"
    }
  }
}