{
  "abstract": "The topological mating of two postcritically finite polynomials with dendritic Julia sets is encoded by a pair of circle laminations $Λ^{\\pm}$, whose collapse produces a sphere-filling curve. When a leaf of $Λ^{+}$ and a leaf of $Λ^{-}$ share an endpoint they form a perfect fit. An unpublished proposition of Epstein, recorded by Petersen and Meyer, shows that for matings of honest degree-$d$ polynomials an infinite-diameter ray equivalence class, i.e. an infinite chain of perfect fits is impossible. We show that this finiteness is a genuinely holomorphic phenomenon. Allowing the dynamics to carry a periodic critical orbit, we construct combinatorially expanding Thurston maps-realized by no expanding rational map-that admit invariant sphere-filling curves yet whose laminations $Λ^{\\pm}$ contain infinite chains of perfect fits, in fact infinitely many of them.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03838",
  "author_total": 1,
  "authors": [
    {
      "name": "Ino Loukidou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5hmddg5w174wn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03838",
  "fulltext_url": null,
  "id": "5hmddg5w174wn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03838",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.03838",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5hmddg5w174wn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03838",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03838"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Infinite chains of perfect fits for expanding Thurston maps",
  "title_text": "Infinite chains of perfect fits for expanding Thurston maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/5hmddg5w174wn",
  "venue": "arXiv",
  "versions": []
}