{
  "id": "0710.4004",
  "version": "v1",
  "published": "2007-10-22T09:52:18.000Z",
  "updated": "2007-10-22T09:52:18.000Z",
  "title": "The N-Vortex Problem on a Symmetric Ellipsoid: A Perturbation Approach",
  "authors": [
    "Cesar Castilho",
    "Helio Machado"
  ],
  "comment": "14 pages, 1 figure",
  "doi": "10.1063/1.2863515",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the N-vortex problem on a ellipsoid of revolution. Applying standard techniques of classical perturbation theory we construct a sequence of conformal transformations from the ellipsoid into the complex plane. Using these transformations the equations of motion for the N-vortex problem on the ellipsoid are written as a formal series on the eccentricity of the ellipsoid's generating ellipse. First order equations are obtained explicitly. We show numerically that the truncated first order system for the three-vortices system on the symmetric ellipsoid is non-integrable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-10-22T09:52:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76C05",
      "58F40"
    ],
    "keywords": [
      "n-vortex problem",
      "symmetric ellipsoid",
      "perturbation approach",
      "truncated first order system",
      "first order equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Mathematical Physics",
      "year": 2008,
      "month": "Feb",
      "volume": 49,
      "number": 2,
      "pages": "022703"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JMP....49b2703C"
    }
  }
}