2 research outputs found
Non-autonomous Hamiltonian systems related to highest Hitchin integrals
We describe non-autonomous Hamiltonian systems coming from the Hitchin
integrable systems. The Hitchin integrals of motion depend on the W-structures
of the basic curve. The parameters of the W-structures play the role of times.
In particular, the quadratic integrals dependent on the complex structure
(W_2-structure) of the basic curve and times are coordinate on the Teichmuller
space. The corresponding flows are the monodromy preserving equations such as
the Schlesinger equations, the Painleve VI equation and their generalizations.
The equations corresponding to the highest integrals are monodromy preserving
conditions with respect to changing of the W_k-structures (k>2). They are
derived by the symplectic reduction from the gauge field theory on the basic
curve interacting with W_k-gravity. As by product we obtain the classical Ward
identities in this theory.Comment: 21 pages,Latex, Contribution in the Proceedings "International
Seminar on Integrable systems". In memoriam Mikail V. Saveliev. Bonn,
February, 199