TY - JOUR
T1 - Canonical structure and symmetries of the Schlesinger equations
AU - Dubrovin, Boris
AU - Mazzocco, Marta
PY - 2007/4
Y1 - 2007/4
N2 - 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. © Springer-Verlag 2007.
AB - 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. © Springer-Verlag 2007.
UR - https://www.scopus.com/pages/publications/33847670520
U2 - 10.1007/s00220-006-0165-3
DO - 10.1007/s00220-006-0165-3
M3 - Article
SN - 1432-0916
VL - 271
SP - 289
EP - 373
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -