{
  "id": "1801.00023",
  "version": "v1",
  "published": "2017-12-29T19:41:21.000Z",
  "updated": "2017-12-29T19:41:21.000Z",
  "title": "Exceptional sets for nonuniformly hyperbolic diffeomorphisms",
  "authors": [
    "Sara Campos",
    "Katrin Gelfert"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For a surface diffeomorphism, a compact invariant locally maximal set $W$ and some subset $A\\subset W$ we study the $A$-exceptional set, that is, the set of points whose orbits do not accumulate at $A$. We show that if the Hausdorff dimension of $A$ is smaller than the Hausdorff dimension $d$ of some ergodic hyperbolic measure, then the topological entropy of the exceptional set is at least the entropy of this measure and its Hausdorff dimension is at least $d$. Particular consequences occur when there is some a priori defined hyperbolic structure on $W$ and, for example, if there exists an SRB measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-29T19:41:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional set",
      "nonuniformly hyperbolic diffeomorphisms",
      "hausdorff dimension",
      "compact invariant locally maximal set",
      "priori defined hyperbolic structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}