{
  "abstract": "Using degenerations of rational maps and local asymptotics of periodic multipliers, we prove that for every $d\\ge 2$, the multipliers of any $2d-2$ distinct periodic orbits of degree $d$ rational maps are algebraically independent over $\\mathbb C$, provided that at most $d$ of the selected orbits are fixed points. This condition is sharp because of the Holomorphic Index Formula that relates the multipliers of the $d+1$ fixed points. The result of this paper removes the additional restrictions on periods present in earlier work. The proof proceeds by induction on the degree, using a one-hole degeneration for the induction step and a three-hole degeneration in an exceptional degree four case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06200",
  "author_total": 1,
  "authors": [
    {
      "name": "Igors Gorbovickis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fg2s1tvn4yqrd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06200",
  "fulltext_url": null,
  "id": "fg2s1tvn4yqrd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06200",
  "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": "W7211992004",
  "pdf_url": "https://arxiv.org/pdf/2609.06200",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fg2s1tvn4yqrd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06200",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06200"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Independence of multipliers via degenerations of rational maps",
  "title_text": "Independence of multipliers via degenerations of rational maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/fg2s1tvn4yqrd",
  "venue": "arXiv",
  "versions": []
}