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2007.46: Canonical structure and symmetries of the Schlesinger equations

2007.46: B. Dubrovin and M. Mazzocco (2007) Canonical structure and symmetries of the Schlesinger equations. Communications in Mathematical Physics, 271 (2). pp. 289-373. ISSN 1432-0916

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DOI: 10.1007/s00220-006-0165-3

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 × 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.

Item Type:Article
Subjects:MSC 2000 > 34 Ordinary differential equations
MIMS number:2007.46
Deposited By:Miss Louise Stait
Deposited On:29 March 2007

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