Canonical structure and symmetries of the Schlesinger equations

Dubrovin, B. and Mazzocco, M. (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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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 2010, the AMS's Mathematics Subject Classification > 34 Ordinary differential equations
Depositing User:	Ms Lucy van Russelt
Date Deposited:	29 Mar 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/744

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