{
  "id": "1207.2872",
  "version": "v3",
  "published": "2012-07-12T08:30:44.000Z",
  "updated": "2013-12-03T03:36:45.000Z",
  "title": "The topological complexity of Cantor attractors for unimodal interval maps",
  "authors": [
    "Simin Li",
    "Weixiao Shen"
  ],
  "comment": "33 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a non-flat $C^3$ unimodal map with a Cantor attractor, we show that for any open cover $\\mathcal U$ of this attractor, the complexity function $p(\\mathcal U, n)$ is of order $n\\log n$. In the appendix, we construct a non-renormalizable map with a Cantor attractor for which $p(\\mathcal{U}, n)$ is bounded from above for any open cover $\\mathcal{U}$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-12-03T03:36:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cantor attractor",
      "unimodal interval maps",
      "topological complexity",
      "open cover",
      "complexity function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2872L"
    }
  }
}