{
  "abstract": "We study the Bernoulli property for skew products of the form $f(x,y)=(g(x),A(x)y)$ on $M\\times PSL_2(\\mathbb{R})/Γ$, where $g$ is a smooth, measure-preserving, exponentially mixing diffeomorphism, $Γ<PSL_2(\\mathbb{R})$ is a cocompact lattice, and $A\\colon M\\to \\operatorname{PSL}_2(\\mathbb{R})$ is a $C^{1+α}$ cocycle. We prove that if $A$ has a nonzero Lyapunov exponent, then $f$ is Bernoulli. The proof does not require that $f$ be exponentially mixing. This provides a new method for establishing the Bernoulli property, which applies to a large class of skew products.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08017",
  "author_total": 1,
  "authors": [
    {
      "name": "Meg Doucette"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5xd5r8vmx4v23.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08017",
  "fulltext_url": null,
  "id": "5xd5r8vmx4v23",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08017",
  "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": "W7212030943",
  "pdf_url": "https://arxiv.org/pdf/2609.08017",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5xd5r8vmx4v23.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08017",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08017"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "The Bernoulli property for $PSL_2\\mathbb{R}$ skew products over exponentially mixing base",
  "title_text": "The Bernoulli property for PSL_2ℝ skew products over exponentially mixing base",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/5xd5r8vmx4v23",
  "venue": "arXiv",
  "versions": []
}