{
  "id": "1808.00512",
  "version": "v1",
  "published": "2018-08-01T19:05:46.000Z",
  "updated": "2018-08-01T19:05:46.000Z",
  "title": "Time-dependent polynomials with one multiple root and new solvable dynamical systems",
  "authors": [
    "Oksana Bihun"
  ],
  "categories": [
    "math-ph",
    "math.CA",
    "math.DS",
    "math.MP"
  ],
  "abstract": "A time-dependent monic polynomial in the z variable with N distinct roots such that exactly one root has multiplicity m>=2 is considered. For k=1,2, the k-th derivatives of the N roots are expressed in terms of the derivatives of order j<= k of the first N coefficients of the polynomial and of the derivatives of order j<= k-1 of the roots themselves. These relations are utilized to construct new classes of algebraically solvable first order systems of ODEs as well as N-body problems. Multiple examples of solvable isochronous (all solutions are periodic with the same period) 2- and 3-body problems are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-01T19:05:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70F10",
      "70K42"
    ],
    "keywords": [
      "solvable dynamical systems",
      "time-dependent polynomials",
      "multiple root",
      "algebraically solvable first order systems",
      "time-dependent monic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}