{
  "id": "0902.4649",
  "version": "v1",
  "published": "2009-02-26T17:49:00.000Z",
  "updated": "2009-02-26T17:49:00.000Z",
  "title": "Inverse Approach In The Study Of Ordinary Differential Equations",
  "authors": [
    "Rafael Ramirez",
    "Natalia Sadovskaia"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We extend the Eruguin result exposed in the paper \"Construction of the whole set of ordinary differential equations with a given integral curve\" published in 1952 and construct a differential system in $\\Bbb{R}^N$ which admits a given set of the partial integrals, in particular we study the case when theses functions are polynomials. We construct a non-Darboux integrable planar polynomial system of degree $n$ with one invariant irreducible algebraic curve $g(x,y)=0$. For this system we analyze the Darboux integrability, Poincare's problem and 16th's Hilbert problem for algebraic limit cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-26T17:49:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P25",
      "34C05",
      "34A34"
    ],
    "keywords": [
      "ordinary differential equations",
      "inverse approach",
      "non-darboux integrable planar polynomial system",
      "invariant irreducible algebraic curve",
      "16ths hilbert problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4649R"
    }
  }
}