{
  "id": "math/0306282",
  "version": "v1",
  "published": "2003-06-19T08:12:11.000Z",
  "updated": "2003-06-19T08:12:11.000Z",
  "title": "Stable sets, hyperbolicity and dimension",
  "authors": [
    "Rasul Shafikov",
    "Christian Wolf"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this note we derive an upper bound for the Hausdorff dimension of the stable set of a hyperbolic set $\\Lambda$ of a $C^2$ diffeomorphisms on a $n$-dimensional manifold. As a consequence we obtain that $\\dim_H W^s(\\Lambda)=n$ is equivalent to the existence of a SRB-measure. We also discuss related results in the case of expanding maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-19T08:12:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45"
    ],
    "keywords": [
      "stable set",
      "hyperbolicity",
      "upper bound",
      "hausdorff dimension",
      "hyperbolic set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6282S"
    }
  }
}