{
  "abstract": "We present a computer-assisted approach for proving period-doubling bifurcations in one-parameter families of maps $x \\mapsto f(x,λ)$ on $\\mathbb{R}^n$. We solve a square augmented system, called the period-doubling map, whose unknowns are the fixed point, the parameter, the right eigenvector attached to the eigenvalue $-1$, the left eigenvector with its eigenvalue, and the vector which describes the center manifold to second order. A contraction argument gives a solution close to a numerical approximation, at which the Jacobian is invertible. The determinant of this Jacobian factors into a simple expression, so that it is nonzero exactly when $1$ is not an eigenvalue and $-1$ is a simple eigenvalue crossing the unit circle transversally. Apart from the sign of the cubic normal-form coefficient, computed afterwards, it remains to check with Gershgorin disks that no other eigenvalue lies on the unit circle. The method is applied to a $10$-mode Galerkin projection of the Kot--Schaffer growth-dispersal model, for which we prove a supercritical period-doubling bifurcation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22986",
  "author_total": 2,
  "authors": [
    {
      "name": "Olivier Hénot"
    },
    {
      "name": "Jean-Philippe Lessard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3z7h6rtwr8azf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22986",
  "fulltext_url": null,
  "id": "3z7h6rtwr8azf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22986",
  "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",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7222944733",
  "pdf_url": "https://arxiv.org/pdf/2610.22986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3z7h6rtwr8azf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22986"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Rigorous verification of period-doubling bifurcations in maps",
  "title_text": "Rigorous verification of period-doubling bifurcations in maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/3z7h6rtwr8azf",
  "venue": "arXiv",
  "versions": []
}