{
  "abstract": "In this paper, we establish the classical Brin-Katok local entropy formula for $C^1$ random dynamical systems on a complete Riemannian manifold (possibly non-compact) under a mild integrability condition. The proof depends on the constructions of measurable partitions adapted to asymptotically varying radii and finite measurable partitions with null-boundaries. As an application, under additional integrability assumptions, we obtain the Margulis-Ruelle inequality for $C^2$ random dynamical systems on complete non-compact Riemannian manifolds. Furthermore, we also construct a counterexample showing that the integrability condition above cannot in general be omitted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01896",
  "author_total": 2,
  "authors": [
    {
      "name": "Zeng Lian"
    },
    {
      "name": "Jianhua Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ba402awzz4agk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01896",
  "fulltext_url": null,
  "id": "ba402awzz4agk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01896",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ba402awzz4agk.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01896"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "The Brin-Katok local entropy formula for non-compact random dynamical systems and an application",
  "title_text": "The Brin-Katok local entropy formula for non-compact random dynamical systems and an application",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ba402awzz4agk",
  "venue": "arXiv",
  "versions": []
}