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Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations. (English) Zbl 1044.70010
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.

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
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