{
  "abstract": "For a countably infinite discrete group $G$, we study subsets of $G$ that contain a neighbourhood return-time set of a minimal point in a $G$-flow $X$. For $e\\in F\\subseteq G$, we characterize this property by the existence of $e\\in A\\subseteq F$ such that $\\operatorname{Int}_K(A):=\\{t\\in G:Kt\\subseteq A\\}$ is right syndetic for every finite $K\\subseteq A$, and equivalently by the support of a minimal binary configuration in the Bernoulli shift $2^G$. Additional conditions on $\\operatorname{Int}_K(A) \\operatorname{Int}_K(A)^{-1}$ characterize realization by minimal flows that are weakly mixing of all finite orders or strongly mixing: for every such $K$, the former requires that for each finite $H\\subseteq G$ there is $c\\in G$ with $HcH\\subseteq \\operatorname{Int}_K(A) \\operatorname{Int}_K(A) ^{-1}$, whereas the latter requires that $\\operatorname{Int}_K(A)\\operatorname{Int}_K(A)^{-1}$ be cofinite. We also construct, for every compact metrizable minimal $G$-flow, a free minimal, strongly mixing Cantor flow disjoint from it.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30554",
  "author_total": 2,
  "authors": [
    {
      "name": "Jian Li"
    },
    {
      "name": "Yini Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0exy3ga1k987j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30554",
  "fulltext_url": null,
  "id": "0exy3ga1k987j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30554",
  "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": "W7223260279",
  "pdf_url": "https://arxiv.org/pdf/2610.30554",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0exy3ga1k987j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30554",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30554"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Return Time Sets of Minimal Points for Countable Group Actions",
  "title_text": "Return Time Sets of Minimal Points for Countable Group Actions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/0exy3ga1k987j",
  "venue": "arXiv",
  "versions": []
}