{
  "id": "1710.03369",
  "version": "v1",
  "published": "2017-10-10T01:21:05.000Z",
  "updated": "2017-10-10T01:21:05.000Z",
  "title": "Maps in Dimension One with Infinite Entropy",
  "authors": [
    "Peter Hazard"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We give examples of endomorphisms in dimension one with infinite topological entropy which are $\\alpha$-H\\\"older and $(1,p)$-Sobolev for all $0\\leq\\alpha<1$ and $1\\leq p<\\infty$. This is constructed within a family of endomorphisms with infinite topological entropy and which traverse all $\\alpha$-H\\\"older and $(1,p)$-Sobolev classes. Finally, we also give examples of endomorphisms, also in dimension one, which lie in the big and little Zygmund classes, answering a question of M. Benedicks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-10T01:21:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B40",
      "37E99",
      "46E35",
      "26A16"
    ],
    "keywords": [
      "infinite entropy",
      "infinite topological entropy",
      "little zygmund classes",
      "endomorphisms",
      "sobolev classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}