{
  "id": "1709.02431",
  "version": "v1",
  "published": "2017-09-07T19:57:00.000Z",
  "updated": "2017-09-07T19:57:00.000Z",
  "title": "Genericity of Infinite Entropy for Maps with Low Regularity",
  "authors": [
    "Edson de Faria",
    "Peter Hazard",
    "Charles Tresser"
  ],
  "comment": "51 pages, 5 figures. Comments Welcome!",
  "categories": [
    "math.DS"
  ],
  "abstract": "For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the closure of the space of bi-Lipschitz homeomorphisms, with respect to either the H\\\"older or the Sobolev topologies, topological entropy is generically infinite. We also prove versions of the $C^1$-Closing Lemma in either of these spaces. Finally, we give examples of homeomorphisms with infinite topological entropy which are H\\\"older and/or Sobolev of every exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-07T19:57:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B40",
      "37E99",
      "46E35",
      "26A16"
    ],
    "keywords": [
      "low regularity",
      "infinite entropy",
      "bi-lipschitz homeomorphisms",
      "genericity",
      "compact manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}