{
  "abstract": "We establish that for a $C^r$-generic surface repeller ($1 < r \\leq \\infty$), its Hausdorff and box dimensions are exactly the unique zero of the sub-additive topological pressure function. As an application of our framework, we show that the attractor of a uniformly non-conformal and weakly irreducible planar non-linear iterated function system (IFS) satisfying the strong separation condition (SSC) attains its expected Hausdorff and box dimensions. Furthermore, as a direct consequence of our generic repeller theorem, we deduce that this dimension formula also holds for a generic $C^r$ planar IFS satisfying the SSC. Using this approach, we also extend the dichotomy result for graphs of Weierstrass-type functions of Ren and Shen (2021) by weakening their real-analytic requirement to arbitrary $C^r$ regularity for $r > 1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30744",
  "author_total": 4,
  "authors": [
    {
      "name": "Jialun Li"
    },
    {
      "name": "Wenyu Pan"
    },
    {
      "name": "Yao Tong"
    },
    {
      "name": "Disheng Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3r1dawyt7bbkc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30744",
  "fulltext_url": null,
  "id": "3r1dawyt7bbkc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30744",
  "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": "W7204954079",
  "pdf_url": "https://arxiv.org/pdf/2608.30744",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3r1dawyt7bbkc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30744",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30744"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Dimensions of surface repellers and attractors of non-linear planar IFSs",
  "title_text": "Dimensions of surface repellers and attractors of non-linear planar IFSs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/3r1dawyt7bbkc",
  "venue": "arXiv",
  "versions": []
}