{
  "id": "1607.02010",
  "version": "v1",
  "published": "2016-07-07T13:44:06.000Z",
  "updated": "2016-07-07T13:44:06.000Z",
  "title": "Topological invariance of the Collet-Eckmann condition for one-dimensional maps",
  "authors": [
    "Huaibin Li"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper is devoted to study the topological invariance of several non-uniform hyperbolicity conditions of one-dimensional maps. In contrast with the case of maps with only one critical point, it is known that for maps with several critical points the Collet-Eckmann condition is not in itself invariance under topological conjugacy. We show that the Collet-Eckmann condition together with any of several slow recurrence conditions is invariant under topological conjugacy. This extends and gives a new proof of a result by Luzzatto and Wang that also applies to the complex setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-07T13:44:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "collet-eckmann condition",
      "one-dimensional maps",
      "topological invariance",
      "non-uniform hyperbolicity conditions",
      "topological conjugacy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}