Krichever, I. Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations. (English) Zbl 1044.70010 Mosc. Math. J. 2, No. 4, 717-752 (2002). Summary: We construct the Hamiltonian theory of isomonodromy equations for meromorphic connections with irregular singularities on algebraic curves. We obtain an explicit formula for symplectic structure on the space of monodromy and Stokes matrices. From these we derive Whitham equations for isomonodromy equations. It is shown that they provide a flat connection on the space of spectral curves of Hitchin systems. Cited in 4 ReviewsCited in 33 Documents MSC: 70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics 14H50 Plane and space curves Keywords:meromorphic connections; monodromy matrices; symplectic form × Cite Format Result Cite Review PDF Full Text: arXiv