{
  "abstract": "We disprove the unrestricted form of Eden's conjecture, which asserts that the maximal local Lyapunov dimension on a compact global attractor is attained at an equilibrium or a periodic orbit. For each $c>4$, we construct a polynomial differential equation on $\\mathbb{R}^5$ with uniformly negative divergence. Its compact global attractor has Lyapunov dimension $4+4/c$, attained precisely on an invariant two-torus carrying an irrational linear flow. The maximum over all equilibria and periodic orbits is $3$. These conclusions hold both for the local dimension defined by singular values at every positive time and for the asymptotic Kaplan--Yorke dimension. The proof uses an exact singular-value identity on the whole attractor. The results of this paper are also formally verified in Lean.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Matthew J. Colbrook"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahacb9mex98sy.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "ahacb9mex98sy",
  "issns": [],
  "landing_url": "https://hal.science/hal-05757958v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05757958/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahacb9mex98sy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:37Z",
      "native_id": "hal-05757958",
      "source": "hal",
      "url": "https://hal.science/hal-05757958v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Aperiodic maximisers of Lyapunov dimension: A counterexample to the unrestricted form of Eden's conjecture",
  "title_text": "Aperiodic maximisers of Lyapunov dimension: A counterexample to the unrestricted form of Eden's conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:37Z",
  "url": "https://research.draconitic.com/paper/ahacb9mex98sy",
  "venue": "HAL",
  "versions": []
}