{
  "abstract": "We prove that for all degree $d\\geq 2$ and all bounded type irrational $θ$, in the space of monic polynomials having a period $1$ Siegel disk $Δ$ of rotation number $θ$, the maximum locus of the conformal radius of $Δ$ with respect to its fixed point contains polynomials having all critical points on the boundary of $Δ$. We apply this to reduce a conjecture of Douady (optimality of the Bruno condition) to a weaker statement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.24833",
  "author_total": 3,
  "authors": [
    {
      "name": "Xavier Buff"
    },
    {
      "name": "Arnaud Chéritat"
    },
    {
      "name": "Pascale Roesch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cf21q3s70rkfd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.24833",
  "fulltext_url": null,
  "id": "cf21q3s70rkfd",
  "issns": [],
  "landing_url": "https://hal.science/hal-05738283v1",
  "language": "en",
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7165731621",
  "pdf_url": "https://arxiv.org/pdf/2606.24833",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cf21q3s70rkfd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:27Z",
      "native_id": "hal-05738283",
      "source": "hal",
      "url": "https://hal.science/hal-05738283v1"
    },
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2606.24833",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.24833"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Biggest bounded type Siegel disks of monic polynomials include those that stick to all critical points",
  "title_text": "Biggest bounded type Siegel disks of monic polynomials include those that stick to all critical points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/cf21q3s70rkfd",
  "venue": "HAL",
  "versions": []
}