{
  "id": "math/0311261",
  "version": "v4",
  "published": "2003-11-16T16:37:09.000Z",
  "updated": "2007-01-10T14:29:09.000Z",
  "title": "Canonical structure and symmetries of the Schlesinger equations",
  "authors": [
    "Boris Dubrovin",
    "Marta Mazzocco"
  ],
  "comment": "92 pages, no figures. Theorem 1.2 corrected, other misprints removed. To appear on Comm. Math. Phys",
  "categories": [
    "math.DG",
    "math.CA",
    "nlin.SI"
  ],
  "abstract": "The Schlesinger equations $S_{(n,m)}$ describe monodromy preserving deformations of order $m$ Fuchsian systems with $n+1$ poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of $n$ copies of $m\\times m$ matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation of the general Schlesinger equations $S_{(n,m)}$ for all $n$, $m$ and we compute the action of the symmetries of the Schlesinger equations in these coordinates.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-01-10T14:29:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G34",
      "34M55",
      "53D30"
    ],
    "keywords": [
      "canonical structure",
      "symmetries",
      "standard linear poisson bracket",
      "commuting time-dependent hamiltonian systems",
      "general schlesinger equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 92,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....11261D"
    }
  }
}