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This article is cited in 34 scientific papers (total in 34 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
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.
DOI:
https://doi.org/10.17323/1609-4514-2002-2-4-717-752
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http://www.ams.org/.../abst2-4-2002.html
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MSC: 14, 79
Received: February 18, 2002; in revised form April 20, 2002
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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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\yr 2002
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\pages 717--752
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