{
  "abstract": "Let $f(z,w)=(p(z),q(z,w))$ be a polynomial skew product of $\\mathbb{C}^2$ of degree $d\\geqslant 2$ and let $μ$ and $μ_p$ be the Green measures associated to $f$ and $p$ respectively. Let $λ_1 > λ_2$ and $λ_p$ be the Lyapunov exponents of $(f,μ)$ and $(p,μ_p)$ respectively. We show that if $λ_2 = λ_p$, then $μ$ is exact dimensional and: \\begin{equation*}\\dim_Hμ=\\frac{\\log d}{λ_1}+\\frac{\\log d}{λ_2}.\\end{equation*} The proof relies on the continuity of the conditional measures obtained by Jonsson, on the fact that $μ$ has constant Jacobian $d^2$, and on a fibered version of a normal form theorem for the inverse branches of the iterates of $f$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19812",
  "author_total": 1,
  "authors": [
    {
      "name": "Clara Genes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6xqdknrrf5xf2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19812",
  "fulltext_url": null,
  "id": "6xqdknrrf5xf2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19812",
  "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.CV"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7222312929",
  "pdf_url": "https://arxiv.org/pdf/2610.19812",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6xqdknrrf5xf2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19812",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19812"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Dimension of the Green measure of skew products with dominant exponent in the fibers",
  "title_text": "Dimension of the Green measure of skew products with dominant exponent in the fibers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/6xqdknrrf5xf2",
  "venue": "arXiv",
  "versions": []
}