{
  "id": "1506.00676",
  "version": "v1",
  "published": "2015-06-01T21:06:59.000Z",
  "updated": "2015-06-01T21:06:59.000Z",
  "title": "Exceptional sets for nonuniformly expanding maps",
  "authors": [
    "Sara Campos",
    "Katrin Gelfert"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Given a rational map of the Riemann sphere and a subset $A$ of its Julia set, we study the $A$-exceptional set, that is, the set of points whose orbit does not accumulate at $A$. We prove that if the Hausdorff dimension of $A$ is smaller than the dynamical dimension of the system then the Hausdorff dimension of the $A$-exceptional set is larger than or equal to the dynamical dimension, with equality in the particular case when the map is expansive. Furthermore, if the topological entropy of $A$ is less than the topological entropy of the full system then the $A$-exceptional set has full topological entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-01T21:06:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional set",
      "nonuniformly expanding maps",
      "hausdorff dimension",
      "dynamical dimension",
      "julia set"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/29/4/1238",
      "journal": "Nonlinearity",
      "year": 2016,
      "month": "Apr",
      "volume": 29,
      "number": 4,
      "pages": 1238
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016Nonli..29.1238C"
    }
  }
}