{
  "abstract": "Let $\\{f_i(x)=M_ix+a_i\\}_{i\\in I}$ be an affine iterated function system on $\\mathbb{R}^d$ with attractor $Λ$, and let $μ$ be an associated self-affine measure. Assume that the $M_i$ generate a Zariski dense subgroup of $\\mathrm{GL}_d(\\mathbb{R})$. Under the strong open set condition, we show that $\\dim_{\\mathrm{H}}Λ$ equals the affinity dimension and that $\\dim_{\\mathrm{H}}μ$ equals the Lyapunov dimension. The above results are consequences of the following projection theorem, which requires no separation condition. For every $1\\leq n\\leq d$ and for Furstenberg measure a.e. $(d-n)$-dimensional subspace $V$, \\[ \\dim_{\\mathrm{H}} (P^V)_*μ=\\min\\{n,\\,\\dim_{\\mathrm{H}}μ\\}. \\] This projection theorem in fact holds under hypotheses weaker than Zariski density: simplicity of the Lyapunov spectrum and a mild transversality condition (the Oseledets non-concentration property). The source of dimension increment in our proof is the positive dimension of the fiberwise conditional measures, exploited through Wu's one-dimensional entropy increase theorem. A key ingredient in reducing the higher-dimensional problem to this setting is a new structural result: a slab-filling property of the measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15485",
  "author_total": 3,
  "authors": [
    {
      "name": "Jialun Li"
    },
    {
      "name": "Wenyu Pan"
    },
    {
      "name": "Zhiyuan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ag1nrrk33zmb2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15485",
  "fulltext_url": null,
  "id": "ag1nrrk33zmb2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15485",
  "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": "W7221800283",
  "pdf_url": "https://arxiv.org/pdf/2610.15485",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ag1nrrk33zmb2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15485",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15485"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Dimension of affine iterated function systems on $\\mathbb{R}^d$",
  "title_text": "Dimension of affine iterated function systems on ℝ^d",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/ag1nrrk33zmb2",
  "venue": "arXiv",
  "versions": []
}