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Canonical structure and symmetries of the Schlesinger equations | | Boris Dubrovin
; Marta Mazzocco
; | | Date: |
16 Nov 2003 | | Subject: | Differential Geometry; Classical Analysis and ODEs; Exactly Solvable and Integrable Systems MSC-class: 32G34 (Primary); 34M55, 53D30 (Secondary) | 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 $m imes m$ 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. | | Source: | arXiv, math.DG/0311261 | | Services: | Forum | Review | PDF | Favorites | |
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