{
  "id": "1408.0223",
  "version": "v2",
  "published": "2014-08-01T16:23:58.000Z",
  "updated": "2015-01-26T20:35:18.000Z",
  "title": "Central Strips of Sibling Leaves in Laminations of the Unit Disk",
  "authors": [
    "David J. Cosper",
    "Jeffrey K. Houghton",
    "John C. Mayer",
    "Luka Mernik",
    "Joseph W. Olson"
  ],
  "comment": "31 pages and 19 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "Quadratic laminations of the unit disk were introduced by Thurston as a vehicle for understanding the (connected) Julia sets of quadratic polynomials and the parameter space of quadratic polynomials. The \"Central Strip Lemma\" plays a key role in Thurston's classification of gaps in quadratic laminations, and in describing the corresponding parameter space. We generalize the notion of {\\em Central Strip} to laminations of all degrees $d\\ge2$ and prove a Central Strip Lemma for degree $d\\ge2$. We conclude with applications of the Central Strip Lemma to {\\em identity return polygons} that show it may play a role similar to Thurston's lemma for higher degree laminations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-01T16:23:58.000Z",
      "comment": "30 pages and 18 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-26T20:35:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F20",
      "54F15"
    ],
    "keywords": [
      "unit disk",
      "central strip lemma",
      "sibling leaves",
      "quadratic laminations",
      "parameter space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.0223C"
    }
  }
}