{
  "id": "math-ph/0307013",
  "version": "v1",
  "published": "2003-07-08T17:29:44.000Z",
  "updated": "2003-07-08T17:29:44.000Z",
  "title": "Classical Dynamical Systems from q-algebras:\"cluster\" variables and explicit solutions",
  "authors": [
    "Angel Ballesteros",
    "Orlando Ragnisco"
  ],
  "comment": "19 Latex pages, No figures",
  "doi": "10.1088/0305-4470/36/42/007",
  "categories": [
    "math-ph",
    "math.MP",
    "math.QA",
    "nlin.SI"
  ],
  "abstract": "A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra. In this way several examples of N-body dynamical systems obtained from q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2) Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of Ruijsenaars type arising from the same (non co-boundary) q-deformation of the (1+1) Poincare' algebra. Also, a unified interpretation of all these systems as different Poisson-Lie dynamics on the same three dimensional solvable Lie group is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-07-08T17:29:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "explicit solution",
      "classical dynamical systems",
      "q-algebras",
      "n-body classical hamiltonian systems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}