{
  "id": "2405.04281",
  "version": "v1",
  "published": "2024-05-07T12:49:25.000Z",
  "updated": "2024-05-07T12:49:25.000Z",
  "title": "On a variant of Hilbert's 16th problem",
  "authors": [
    "Armengol Gasull",
    "Paulo Santana"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the number of limit cycles that a planar polynomial vector field can have as a function of its number $m$ of monomials. We prove that the number of limit cycles increases at least quadratically with $m$ and we provide good lower bounds for $m\\le10.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-07T12:49:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilberts 16th problem",
      "planar polynomial vector field",
      "limit cycles increases",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}