{
  "abstract": "We study the skew product systems $T: \\mathbb{S}^1\\times\\mathbb{R}^d \\to \\mathbb{S}^1 \\times\\mathbb{R}^d$, \\begin{equation*} T(x,y)=(\\ell x, A y+ϕ(x)), \\end{equation*} where $\\ell\\geq 2,$ $A \\in GL_d(\\mathbb{R})$ with $ρ(A)<1$, and $ϕ\\in C^r(\\mathbb{S}^1, \\mathbb{R}^d)$, with $r>(d+3)/2. We allow the fibers to have any dimension and $A$ to be non-conformal. We show that: when $|\\det(A)|\\ell<1$, for almost every $ϕ$, the Hausdorff dimension of the solenoid attractor and the SRB measure equal 1+ the affinity dimension; when $|\\det(A)|\\ell>1$, for almost every $ϕ$, the SRB measure is absolutely continuous. In the latter case we investigate the Sobolev regularity of the density of the SRB measure. We introduce a derivative dispersion condition, replacing the usual transversality condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.27089",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniele Galli"
    },
    {
      "name": "Eleonora Passaglia"
    },
    {
      "name": "Andrea Ulliana"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ca5aj3e8qjx3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.27089",
  "fulltext_url": null,
  "id": "9ca5aj3e8qjx3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.27089",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7171782401",
  "pdf_url": "https://arxiv.org/pdf/2607.27089",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ca5aj3e8qjx3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2607.27089",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.27089"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Geometric Properties of Higher Dimensional Solenoidal Attractors",
  "title_text": "Geometric Properties of Higher Dimensional Solenoidal Attractors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/9ca5aj3e8qjx3",
  "venue": "arXiv",
  "versions": []
}