{
  "abstract": "Near a reversible center-center equilibrium, the Birkhoff normal form does not describe the families bifurcating from the continued tori, which resonant normal forms capture through a reduced system.With a reflection symmetry, we develop a coupling normal form in which the bifurcating families also appear as tori of action normal forms. Along a selected coupling direction, the first harmonic in the angle difference is absorbed into an action-dependent counterterm. We prove that the coupled recursion determines unique counterterm coefficients, a formal action normal form, and an exact counterterm factorization. The factorization gives a recovery constraint, whose trivial factor corresponds to the Birkhoff normal form. At every finite order, a symmetric pair of bifurcating branches leaves the trivial branch at a critical curve, carrying approximately invariant tori and circles with residual estimates. In the spatial circular restricted three-body problem, these give approximate halo orbits and quasi-halo tori.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25355",
  "author_total": 1,
  "authors": [
    {
      "name": "Mingpei Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bzvecz9yq1q9n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25355",
  "fulltext_url": null,
  "id": "bzvecz9yq1q9n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25355",
  "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": "W7223052570",
  "pdf_url": "https://arxiv.org/pdf/2610.25355",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bzvecz9yq1q9n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.25355",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25355"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A coupling normal form for reversible center-center Hamiltonians with application to the restricted three-body problem",
  "title_text": "A coupling normal form for reversible center-center Hamiltonians with application to the restricted three-body problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/bzvecz9yq1q9n",
  "venue": "arXiv",
  "versions": []
}