{
  "id": "2005.02195",
  "version": "v1",
  "published": "2020-05-05T14:02:30.000Z",
  "updated": "2020-05-05T14:02:30.000Z",
  "title": "New lower bound for the number of critical periods for planar polynomial systems",
  "authors": [
    "Xiuli Cen"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we construct two classes of planar polynomial Hamiltonian systems having a center at the origin, and obtain the lower bounds for the number of critical periods for these systems. For polynomial potential systems of degree $n$, we provide a lower bound of $n-2$ for the number of critical periods, and for polynomial systems of degree $n$, we acquire a lower bound of $n^2/2+n-5/2$ when $n$ is odd and $n^2/2-2$ when $n$ is even for the number of critical periods. To the best of our knowledge, these lower bounds are new, moreover the latter one is twice the existing results up to the dominant term.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-05T14:02:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "critical periods",
      "planar polynomial systems",
      "planar polynomial hamiltonian systems",
      "polynomial potential systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}