{
  "abstract": "In this paper, we study planar polynomial vector fields admitting invariant circles. We characterize polynomial vector fields having $m$ concentric invariant circles, and we describe those having three invariant circles whose centers are not collinear. We also give a necessary and sufficient condition for the unit circle to be the unique limit cycle of a quadratic vector field. We prove that a cubic or quartic Kolmogorov vector field having the unit circle invariant has no circular limit cycle, and that a quartic vector field with two concentric circular limit cycles has at most three circular limit cycles, this bound being sharp.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33226",
  "author_total": 2,
  "authors": [
    {
      "name": "Supriyo Jana"
    },
    {
      "name": "Soumen Sarkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c89rt263xmmhj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33226",
  "fulltext_url": null,
  "id": "c89rt263xmmhj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33226",
  "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/2610.33226",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c89rt263xmmhj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33226",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33226"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Some remarks on polynomial vector fields in $\\RR^2$",
  "title_text": "Some remarks on polynomial vector fields in RR^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/c89rt263xmmhj",
  "venue": "arXiv",
  "versions": []
}