{
  "abstract": "We give a conformal mating description for the class $Σ_d$ of hyperbolic Schwarz reflections with connected and full filled Julia set; this parallels the recent development in several non-hyperbolic settings. We show that the escaping dynamics of $Σ_d$ can be characterized independently by the class of \\emph{annular Schwarz reflections} we introduce. Our main result is that each $σ\\inΣ_d$ decomposes into a unique hyperbolic polynomial factor and a unique annular Schwarz reflection factor and, conversely, any two such factors may be mated to determine a unique such Schwarz reflection. We also show that annular Schwarz reflections converge to Nielsen maps in suitable settings, connecting the hyperbolic and non-hyperbolic mating descriptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40196",
  "author_total": 1,
  "authors": [
    {
      "name": "Kirill Lazebnik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6jkc8tcrxdgp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40196",
  "fulltext_url": null,
  "id": "f6jkc8tcrxdgp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40196",
  "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"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7215074941",
  "pdf_url": "https://arxiv.org/pdf/2609.40196",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6jkc8tcrxdgp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40196",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40196"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Dynamics of Hyperbolic Schwarz Reflections",
  "title_text": "Dynamics of Hyperbolic Schwarz Reflections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/f6jkc8tcrxdgp",
  "venue": "arXiv",
  "versions": []
}