{
  "abstract": "We prove exact dimensionality of ergodic stationary measures for random compositions of $C^1$ diffeomorphisms of a closed manifold $M$ that contract at a single Lyapunov scale. More precisely, let $ν$ be a Borel probability measure on $\\mathrm{Diff}^1(M)$ such that $\\log\\sup_{x}\\|{D_xf}\\|$ and $\\log\\sup_{x}\\|{D_xf^{-1}}\\|$ are $ν$-integrable, and let $μ$ be an ergodic $ν$-stationary probability measure. If the top and bottom Lyapunov exponents of the derivative cocycle coincide and equal $λ<0$, then $μ$ is exact dimensional and $\\mathrm{dim}(μ)=h_μ^{\\mathrm{F}}(ν)/(-λ)$, where $h_μ^{\\mathrm{F}}(ν)$ is the Furstenberg entropy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10538",
  "author_total": 1,
  "authors": [
    {
      "name": "Subhasish Mukherjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2kexmfvwcxxww.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10538",
  "fulltext_url": null,
  "id": "2kexmfvwcxxww",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10538",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7212120435",
  "pdf_url": "https://arxiv.org/pdf/2609.10538",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2kexmfvwcxxww.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2609.10538",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10538"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Exact dimensionality of stationary measures for random diffeomorphisms with all Lyapunov exponents equal and negative",
  "title_text": "Exact dimensionality of stationary measures for random diffeomorphisms with all Lyapunov exponents equal and negative",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/2kexmfvwcxxww",
  "venue": "arXiv",
  "versions": []
}