{
  "abstract": "We prove strict separation of antiperiodic degeneracy curves associated with elliptic Euler and Lagrangian solutions of the planar three-body problem. For every eccentricity $0<e<1$, each Euler pair issuing from a common circular parameter is strictly ordered in the extended family $β>0$, and the two Lagrangian curves remain disjoint. Every antiperiodic degeneracy point in these families with $0<e<1$ has a one-dimensional full kernel. Rotation and reflection decomposition yield, for each model, two half-integer Fourier block operators with identical tails and different first blocks. In the Euler case, a positive definite first-block perturbation gives a definite connecting crossing form; a spectral-flow rectangle and sectorwise index counts then force strict separation. In the Lagrangian case, exact tail elimination and an explicit estimate for a two-dimensional Schur complement exclude simultaneous degeneracy in the two reflection sectors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01719",
  "author_total": 3,
  "authors": [
    {
      "name": "Xijun Hu"
    },
    {
      "name": "Li Wu"
    },
    {
      "name": "Ao Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4fz7ejt4pr468.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01719",
  "fulltext_url": null,
  "id": "4fz7ejt4pr468",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01719",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01719",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4fz7ejt4pr468.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01719",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01719"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Strict Separation of Antiperiodic Degeneracy Curves for Elliptic Euler and Lagrangian Solutions",
  "title_text": "Strict Separation of Antiperiodic Degeneracy Curves for Elliptic Euler and Lagrangian Solutions",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/4fz7ejt4pr468",
  "venue": "arXiv",
  "versions": []
}