{
  "abstract": "We establish dimension bounds and an exact dimension formula for equilibrium measures of degree $d$ holomorphic endomorphisms of $\\mathbb P^2=\\mathbb P^2(\\mathbb C)$ satisfying suitable expansion and domination conditions. Write $λ_1>λ_2>0$ for their Lyapunov exponents. If two inverse histories ending at the same point determine different fast directions, we prove that ${\\mathrm dim}_H μ_F>\\log d/λ_1+\\log d/λ_2$ when $λ_2>\\log d$, and that ${\\mathrm dim}_H μ_F=2\\log d/λ_2$ when $λ_2\\ge2\\log d$. Applying these results to an explicit quadratic family, we disprove the Binder--DeMarco conjecture on a non-empty open set of holomorphic endomorphisms. The proof adapts the projection growth strategy of Li--Pan--Tong--Xu to the holomorphic setting, combining strong leaf geometry and the Ledrappier--Young theory for endomorphisms with a multidimensional extension of Wu's restricted sum estimate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05602",
  "author_total": 2,
  "authors": [
    {
      "name": "Fabrizio Bianchi"
    },
    {
      "name": "Yan Mary He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/796hk5b1frd0w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05602",
  "fulltext_url": null,
  "id": "796hk5b1frd0w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05602",
  "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": "W7220712140",
  "pdf_url": "https://arxiv.org/pdf/2610.05602",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/796hk5b1frd0w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05602",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05602"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "History-dependent unstable directions and the Binder--DeMarco conjecture",
  "title_text": "History-dependent unstable directions and the Binder--DeMarco conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/796hk5b1frd0w",
  "venue": "arXiv",
  "versions": []
}