{
  "abstract": "We study a class of expanding Markov maps on the unit interval, which includes sofic \\(β\\)-transformations, Gauss maps, tent maps and cookie-cutter maps. We investigate the quantitative recurrence property for points that are dynamically badly approximable, namely, points whose orbits eventually remain a positive distance from a given point. We show that the Hausdorff dimension of the intersection of a recurrence set and a badly approximable set is determined by the same pressure function as that of the corresponding recurrence set. We further obtain the Hausdorff dimensions of two related intersections: recurrence sets with non-recurrent sets, and shrinking target sets with badly approximable sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12258",
  "author_total": 2,
  "authors": [
    {
      "name": "Lingmin Liao"
    },
    {
      "name": "Na Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/652aq3yxns343.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12258",
  "fulltext_url": null,
  "id": "652aq3yxns343",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12258",
  "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": "W7221183746",
  "pdf_url": "https://arxiv.org/pdf/2610.12258",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/652aq3yxns343.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12258",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12258"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Intersections of quantitative recurrence and badly approximable sets for expanding Markov maps",
  "title_text": "Intersections of quantitative recurrence and badly approximable sets for expanding Markov maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/652aq3yxns343",
  "venue": "arXiv",
  "versions": []
}