{
  "id": "1805.08382",
  "version": "v1",
  "published": "2018-05-22T04:15:56.000Z",
  "updated": "2018-05-22T04:15:56.000Z",
  "title": "Geometric and integrability properties of Kahan's method",
  "authors": [
    "Elena Celledoni",
    "David McLaren",
    "Brynjulf Owren",
    "Reinout Quispel"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "Given a quadratic vector field on \\mathbb{R}^n possessing a quadratic first integral depending on two of the independent variables, we give a constructive proof that Kahan's discretization method exactly preserves a nearby modifed integral. Building on this result, we present a family of integrable quadratic vector fields (including the Euler top) whose Kahan discretization is a novel 10-parameter family of integrable maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-22T04:15:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kahans method",
      "integrability properties",
      "kahans discretization method exactly preserves",
      "integrable quadratic vector fields",
      "quadratic first integral"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}