{
  "abstract": "We establish uniform multicritical pseudo-Siegel bounds for polynomials of Zakeri type, where all free critical points are on the boundary of an invariant Siegel disk of bounded type. This generalizes the unicritical result~\\cite{DL:wZ}. As an application, we show the optimality of the Brjuno condition under the Zakeri restriction: as the rotation number becomes non-Brjuno, the Siegel disk evolves into the Cremer Hedgehog. Combined with~\\cite{BCR26}, this implies the optimality of the Brjuno condition for all neutral polynomials, resolving a conjecture by Douady from the 1980s.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37468",
  "author_total": 3,
  "authors": [
    {
      "name": "Dzmitry Dudko"
    },
    {
      "name": "Yusheng Luo"
    },
    {
      "name": "Runze Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0dxrw2em84dp0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37468",
  "fulltext_url": null,
  "id": "0dxrw2em84dp0",
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  "landing_url": "https://arxiv.org/abs/2610.37468",
  "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.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7224114977",
  "pdf_url": "https://arxiv.org/pdf/2610.37468",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0dxrw2em84dp0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37468",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37468"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Multicritical pseudo-Siegel bounds and the optimality of the Brjuno condition for all neutral polynomials",
  "title_text": "Multicritical pseudo-Siegel bounds and the optimality of the Brjuno condition for all neutral polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/0dxrw2em84dp0",
  "venue": "arXiv",
  "versions": []
}