{
  "abstract": "We study Schmidt's game on the Julia set $J(f)$ of weak hyperbolic rational maps $f:\\CC\\to\\CC$. For each $y\\in J(f)$, let $E(f,y)$ be the set of points in $J(f)$ whose forward orbits stay a positive distance from $y$. We prove that $E(f,y)$ is absolute winning on $J(f)$ for each $y \\in J(f)$. To do this, we first prove the absolute winning property for the exceptional set associated to the critical points by a potential game argument, and then use uniform expansion to obtain the result for each target point $y$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27796",
  "author_total": 1,
  "authors": [
    {
      "name": "Haoyang Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4cm1eqcmebby.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27796",
  "fulltext_url": null,
  "id": "b4cm1eqcmebby",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27796",
  "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": "W7223128758",
  "pdf_url": "https://arxiv.org/pdf/2610.27796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4cm1eqcmebby.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27796"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Absolute winning properties of exceptional sets for rational maps",
  "title_text": "Absolute winning properties of exceptional sets for rational maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/b4cm1eqcmebby",
  "venue": "arXiv",
  "versions": []
}