{
  "abstract": "For every fixed real quintic polynomial $F$, we prove that the slow--fast Liénard system $\\dot{x}=y-F(x),\\quad \\dot{y}=-\\varepsilon x$ admits at most two limit cycles whenever $0<\\varepsilon<\\varepsilon_0(F)$ for a suitable $\\varepsilon_0(F)>0$. Using scalar comparison near the equilibrium and a logarithmic fold-passage correction, we exclude \\rev{canard singular limits}. Every sequence of limit cycles with $\\varepsilon\\to0^+$ has a subsequence converging in the Hausdorff metric to a common slow--fast path, whose regular slow arcs are either all normally attracting or all normally repelling. We also establish uniform Floquet separation for fixed $F$. The global counting argument uses shared regular arcs, nesting, and stability alternation. These results give a global small-parameter bound and describe the singular-limit structure, complementing the local cyclicity analysis of Li and Lu(J. Differential Equations, 2014).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13080",
  "author_total": 3,
  "authors": [
    {
      "name": "Hebai Chen"
    },
    {
      "name": "Leshan Chen"
    },
    {
      "name": "Yu Xiao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dcbdfkhn74xq0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13080",
  "fulltext_url": null,
  "id": "dcbdfkhn74xq0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13080",
  "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.CA"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7221521773",
  "pdf_url": "https://arxiv.org/pdf/2610.13080",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dcbdfkhn74xq0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13080",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13080"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Limit cycles of slow-fast quintic Lienard systems",
  "title_text": "Limit cycles of slow-fast quintic Lienard systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/dcbdfkhn74xq0",
  "venue": "arXiv",
  "versions": []
}