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 ofthe 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.

Canonical structure and symmetries of the Schlesinger equations / Dubrovin, Boris; Mazzocco, M.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 271:2(2007), pp. 289-373. [10.1007/s00220-006-0165-3]

Canonical structure and symmetries of the Schlesinger equations

Dubrovin, Boris;
2007-01-01

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 ofthe 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.
2007
271
2
289
373
https://doi.org/10.1007/s00220-006-0165-3
http://preprints.sissa.it/xmlui/handle/1963/1997
Dubrovin, Boris; Mazzocco, M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12565
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