{
  "abstract": "Given a quadratic polynomial with an irrationally indifferent fixed point of bounded type, a bubble is an iterated preimage of its Siegel disk. Similar to pseudo-Siegel disks, one constructs pseudo-bubbles from bubbles by filling in parabolic fjords. We introduce the near-degenerate regime for the $α'$-Dynamics controlling the geometry of these pseudo-bubbles in deep scale. Consequently, we obtain uniform bounds on the size and regularity of pseudo-bubbles independent of the rotation number. In [DLL], jointly with Lyubich, this result serves as a necessary ingredient for establishing uniform butterfly bounds and ultimately the combinatorial rigidity of the full attractor of neutral renormalization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15500",
  "author_total": 2,
  "authors": [
    {
      "name": "Dzmitry Dudko"
    },
    {
      "name": "Willie Rush Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4nbe5xg8b30fr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15500",
  "fulltext_url": null,
  "id": "4nbe5xg8b30fr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15500",
  "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": "W7213370114",
  "pdf_url": "https://arxiv.org/pdf/2609.15500",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4nbe5xg8b30fr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15500",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15500"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Uniform bounds for bubbles of neutral quadratic polynomials",
  "title_text": "Uniform bounds for bubbles of neutral quadratic polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4nbe5xg8b30fr",
  "venue": "arXiv",
  "versions": []
}