{
  "abstract": "Many mechanical systems, such as the Newtonian $n$-body system, are invariant under rotations. The rotational symmetry of the system gives rise to two commuting actions: the dynamical action and the action of the symmetry group. In this paper, we exploit this symmetry to construct families of periodic and quasi-periodic trajectories. In the strong-force setting, we extend Montgomery's variational approach to free homotopy classes of curves that are periodic up to a prescribed nontrivial rotation. In the weak-force setting, we establish, under suitable hypotheses, global and local variational persistence results for action minimizers in loop spaces defined by general finite symmetry-group actions under sufficiently small rotations. As applications, we apply these results to the figure-eight orbit, under a numerically supported assumption of strict local minimality, to double choreographic loops with $q$-fold rotation symmetry, and to counter-rotating double choreographic loops in planar $(N+3)$-body problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10101",
  "author_total": 3,
  "authors": [
    {
      "name": "Hangqi Liang"
    },
    {
      "name": "Zhihong Xia"
    },
    {
      "name": "Tingjie Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3q9tkrm2cv6td.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10101",
  "fulltext_url": null,
  "id": "3q9tkrm2cv6td",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10101",
  "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": "W7220950120",
  "pdf_url": "https://arxiv.org/pdf/2610.10101",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3q9tkrm2cv6td.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10101",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10101"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Variational Persistence of Periodic and Quasi-Periodic Orbits in Symmetric $N$-Body Problems",
  "title_text": "Variational Persistence of Periodic and Quasi-Periodic Orbits in Symmetric N-Body Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/3q9tkrm2cv6td",
  "venue": "arXiv",
  "versions": []
}