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Moscow Mathematical Journal, 2002, Volume 2, Number 4, Pages 717–752
DOI: https://doi.org/10.17323/1609-4514-2002-2-4-717-752 (Mi mmj70) 		 
This article is cited in 45 scientific papers (total in 46 papers)

Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations

I. M. Kricheverabc

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
c Columbia University
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DOI: https://doi.org/10.17323/1609-4514-2002-2-4-717-752
Abstract: We construct the Hamiltonian theory of isomonodromy equations for meromorphic connections with irregular singularities on algebraic curves. We obtain an explicit formula for the symplectic structure on the space of monodromy and Stokes matrices. From these we derive Whitham equations for the isomonodromy equations. It is shown that they provide a flat connection on the space of spectral curves of Hitchin systems.
Key words and phrases: Algebaric curves, meromorphic connections, monodromy matrices, Hamiltonian theory, symplectic form.
Received: February 18, 2002; in revised form April 20, 2002
Bibliographic databases:
MSC: 14, 79
Language: English
Citation: I. M. Krichever, “Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations”, Mosc. Math. J., 2:4 (2002), 717–752
Citation in format AMSBIB
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\by I.~M.~Krichever
\paper Isomonodromy equations on algebraic curves, canonical transformations and Whitham equations
\jour Mosc. Math.~J.
\yr 2002
\vol 2
\issue 4
\pages 717--752
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