{
  "abstract": "We study the number of limit cycles of the piecewise smooth differential system \\[ \\dot{x}=y, \\quad \\dot{y}=-x-\\varepsilon\\bigl(f(x)y+\\operatorname{sgn}(x)g(x,y)\\bigr),\\] where $f(x)$ is a polynomial of degree $n\\geq 1$, $g(x,y)$ is a bivariate polynomial of degree $m\\geq 2$, and $\\varepsilon$ is a sufficiently small parameter. Using the first-order averaging theorem for discontinuous systems, we obtain that the number $H_{m,n}=\\lfloor n/2\\rfloor+\\lfloor m/2\\rfloor$ is a lower bound for the number of limit cycles bifurcating from the linear center $\\dot{x}=y, \\ \\dot{y}=-x$. The bound is sharp, and we provide an explicit example that attains $H_{m,n}$ limit cycles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Qual. Theory Dyn. Syst. 25, 189 (2026)",
  "arxiv": "2609.14140",
  "author_total": 2,
  "authors": [
    {
      "name": "Carlos F. Álvarez"
    },
    {
      "name": "Alexander Sierra-Ortiz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5efr233s2h80f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14140",
  "fulltext_url": null,
  "id": "5efr233s2h80f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14140",
  "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/2609.14140",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5efr233s2h80f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.14140",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14140"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Limit Cycles in a Discontinuous Generalized Liénard Systems with Bivariate Perturbation",
  "title_text": "Limit Cycles in a Discontinuous Generalized Liénard Systems with Bivariate Perturbation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/5efr233s2h80f",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s12346-026-01617-7",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}