{
  "id": "1906.05324",
  "version": "v1",
  "published": "2019-06-12T18:44:34.000Z",
  "updated": "2019-06-12T18:44:34.000Z",
  "title": "Degree-d-invariant laminations",
  "authors": [
    "William P. Thurston",
    "Hyungryul Baik",
    "Yan Gao",
    "John H. Hubbard",
    "Tan Lei",
    "Kathryn A. Lindsey",
    "Dylan P. Thurston"
  ],
  "comment": "62 pages, 24 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "Degree-$d$-invariant laminations of the disk model the dynamical action of a degree-$d$ polynomial; such a lamination defines an equivalence relation on $S^1$ that corresponds to dynamical rays of an associated polynomial landing at the same multi-accessible points in the Julia set. Primitive majors are certain subsets of degree-$d$-invariant laminations consisting of critical leaves and gaps. The space $\\textrm{PM}(d)$ of primitive degree-$d$ majors is a spine for the set of monic degree-$d$ polynomials with distinct roots and serves as a parameterization of a subset of the boundary of the connectedness locus for degree-$d$ polynomials. The core entropy of a postcritically finite polynomial is the topological entropy of the action of the polynomial on the associated Hubbard tree. Core entropy may be computed directly, bypassing the Hubbard tree, using a combinatorial analogue of the Hubbard tree within the context of degree-$d$-invariant laminations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-12T18:44:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "degree-d-invariant laminations",
      "core entropy",
      "combinatorial analogue",
      "connectedness locus",
      "disk model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 62,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}