{
  "abstract": "We prove several necessary and sufficient conditions under which a point satisfies the Poincaré Recurrence Theorem for all computable (ergodic) measure-preserving transformations and all sets of a particular complexity. The necessary conditions are obtained by constructing specific measure-preserving transformations which violate recurrence. While some of these conditions pertain to standard notions of algorithmic randomness, others involve new notions of genericity developed in the context of a computable probability space, which we call $Π^0_n$-genericity and quasi-$Π^0_n$-genericity. We also provide conditions under which points recur at a positive frequency in sets containing them, regarding both simple and multiple recurrence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12402",
  "author_total": 1,
  "authors": [
    {
      "name": "Joey Veltri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4gfm4ygff20a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12402",
  "fulltext_url": null,
  "id": "d4gfm4ygff20a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12402",
  "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"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "1703|Computability, Logic, AI Algorithms"
    ]
  ],
  "openalex": "W7212657246",
  "pdf_url": "https://arxiv.org/pdf/2609.12402",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4gfm4ygff20a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12402",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12402"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Effective recurrence for computable measure-preserving transformations",
  "title_text": "Effective recurrence for computable measure-preserving transformations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/d4gfm4ygff20a",
  "venue": "arXiv",
  "versions": []
}