{
  "abstract": "This paper addresses the problem of Lyapunov stability for equilibrium solutions in periodic Hamiltonian systems under degenerate conditions. The degeneracy occurs in resonant cases when the leading coefficient function in the normal form possesses only zeros of high multiplicity, rendering standard criteria inapplicable. By employing Lie normal form theory, we establish two general stability criteria that resolve the stability problem for nearly all such degenerate scenarios. Our results explicitly demonstrate the decisive role of higher-order terms and provide easily verifiable conditions that generalize several known results in the literature.",
  "abstract_shown": true,
  "affiliations": [
    "School of Mathematics and Statistics, Weifang University, Weifang, Shandong, China"
  ],
  "article_type": "Research Article",
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Nina Xue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7t1en826xrtq2.bib",
  "cited_by": 0,
  "doi": "10.1371/journal.pone.0359575",
  "fulltext_url": null,
  "id": "7t1en826xrtq2",
  "issns": [
    "1932-6203"
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  "landing_url": "https://doi.org/10.1371/journal.pone.0359575",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ],
    [
      "plos",
      "/Computer and information sciences/Systems science/Nonlinear systems"
    ],
    [
      "plos",
      "/Computer and information sciences/Systems science/System instability"
    ],
    [
      "plos",
      "/Computer and information sciences/Systems science/System stability"
    ],
    [
      "plos",
      "/Earth sciences/Geography/Human geography/Human mobility"
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    [
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      "/Engineering and technology/Mechanical engineering/Pendulums"
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      "/Physical sciences/Mathematics/Number theory/Real numbers"
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      "plos",
      "/Physical sciences/Mathematics/Systems science/Nonlinear systems"
    ],
    [
      "plos",
      "/Physical sciences/Mathematics/Systems science/System instability"
    ],
    [
      "plos",
      "/Physical sciences/Mathematics/Systems science/System stability"
    ],
    [
      "plos",
      "/Physical sciences/Physics/Mathematical physics/Equations of motion"
    ],
    [
      "plos",
      "/Physical sciences/Physics/Resonance/Resonance frequency"
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    [
      "plos",
      "/Social sciences/Human geography/Human mobility"
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  "openalex": "W7214743117",
  "pdf_url": "https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0359575&type=printable",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": "Public Library of Science",
  "ris": "https://research.draconitic.com/paper/7t1en826xrtq2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:37Z",
      "native_id": "10.1371/journal.pone.0359575",
      "source": "plos",
      "url": "https://doi.org/10.1371/journal.pone.0359575"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "plos:number theory",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "plos:mathematical physics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On the stability of equilibria in degenerate periodic Hamiltonian systems",
  "title_text": "On the stability of equilibria in degenerate periodic Hamiltonian systems",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:37Z",
  "url": "https://research.draconitic.com/paper/7t1en826xrtq2",
  "venue": "PLOS One",
  "versions": []
}