{
  "abstract": "We study the multifractal analysis of self-affine measures supported on planar carpets of type Gatzouras--Lalley. We work primarily with Olsen's Hausdorff-dimensional variant of the $L^q$ spectrum, which we denote by $\\vartheta(q)$. We prove a variational formula for $\\vartheta$, from which it follows that multifractal formalism holds at all values $q$ for which $\\vartheta(q)$ is differentiable. However, in general, $\\vartheta$ need not be differentiable and the multifractal formalism may fail. In fact, the multifractal spectrum may be non-differentiable and have jump discontinuities in the interior of its support, and there may be multiple phase transitions at both negative and positive values of $q$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35092",
  "author_total": 3,
  "authors": [
    {
      "name": "Thomas Jordan"
    },
    {
      "name": "István Kolossváry"
    },
    {
      "name": "Alex Rutar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/40kw53bpzj83a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35092",
  "fulltext_url": null,
  "id": "40kw53bpzj83a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35092",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214746815",
  "pdf_url": "https://arxiv.org/pdf/2609.35092",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/40kw53bpzj83a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35092",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35092"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Multifractal analysis of Gatzouras--Lalley measures",
  "title_text": "Multifractal analysis of Gatzouras--Lalley measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/40kw53bpzj83a",
  "venue": "arXiv",
  "versions": []
}