{
  "abstract": "We study the relation between uniformly positive entropy and uniformly positive mean dimension at the level of fixed open covers. To a symbolic system X, we associate a hub-and-spoke system Spoke(X), obtained by replacing each symbol by a one-dimensional spoke attached to a common hub. We prove that if X admits a shift-invariant measure of full support, then Spoke(X) has completely positive mean dimension. We also prove that if X has uniformly positive entropy, then Spoke(X) has uniformly positive mean dimension. Finally, using symbolic codings of irrational rotations on tori, we construct hub-and-spoke systems with completely positive mean dimension but without uniformly positive mean dimension or uniformly positive entropy. The examples are nondegenerate: the relevant covers have zero mean dimension and zero entropy, but when refined by iterating under the dynamics the corresponding covering numbers are unbounded.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.01501",
  "author_total": 2,
  "authors": [
    {
      "name": "Tal Barak"
    },
    {
      "name": "Elon Lindenstrauss"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drsqnfh1w0v37.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.01501",
  "fulltext_url": null,
  "id": "drsqnfh1w0v37",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.01501",
  "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": "W7167260913",
  "pdf_url": "https://arxiv.org/pdf/2607.01501",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drsqnfh1w0v37.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2607.01501",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.01501"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Uniformly Positive Mean Dimension",
  "title_text": "Uniformly Positive Mean Dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/drsqnfh1w0v37",
  "venue": "arXiv",
  "versions": []
}