{
  "abstract": "Let $A$ be an $α$-Hölder cocycle over a transitive two-sided subshift of finite type, and assume that $A$ is strongly bunched. We prove that if there exist $k\\in\\{1,\\ldots,d-1\\}$ and $c>0$ such that \\[ λ_k(p)-λ_{k+1}(p)\\ge c \\] for every periodic point $p$, then $A$ admits a dominated splitting of index $k$. Thus, under strong bunching, a uniform asymptotic gap in the Lyapunov spectrum of periodic measures implies a uniform geometric splitting along all orbit segments. This extends the periodic-gap criterion of Kassel--Potrie from locally constant cocycles to Hölder cocycles in arbitrary dimension, and extends the two-dimensional fiber-bunched result of Velozo to higher dimensions under the stronger bunching assumption.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28384",
  "author_total": 1,
  "authors": [
    {
      "name": "Lucas Backes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5dn9m9fd2vtmg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28384",
  "fulltext_url": null,
  "id": "5dn9m9fd2vtmg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28384",
  "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": "W7214231137",
  "pdf_url": "https://arxiv.org/pdf/2609.28384",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5dn9m9fd2vtmg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28384",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28384"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "From a Gap in the Lyapunov Spectrum to Dominated Splittings",
  "title_text": "From a Gap in the Lyapunov Spectrum to Dominated Splittings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/5dn9m9fd2vtmg",
  "venue": "arXiv",
  "versions": []
}