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Mosc. Math. J., 2002, Volume 2, Number 4, Pages 717–752 (Mi mmj70)  

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.


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MSC: 14, 79
Received: February 18, 2002; in revised form April 20, 2002

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
\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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    This publication is cited in the following articles:
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    25. A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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    29. Schlichenmaier M., “Krichever-Novikov Type Algebras: Theory and Applications”, Krichever-Novikov Type Algebras: Theory and Applications, Degruyter Studies in Mathematics, 53, Walter de Gruyter Gmbh, 2014, 1–360  crossref  mathscinet  isi
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    32. Arata Komyo, “The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations”, SIGMA, 14 (2018), 111, 22 pp.  mathnet  crossref
    33. Its A.R., Prokhorov A., “On Some Hamiltonian Properties of the Isomonodromic Tau Functions”, Rev. Math. Phys., 30:7, SI (2018), 1840008  crossref  mathscinet  zmath  isi  scopus
    34. Its A.R., Lisovyy O., Prokhorov A., “Monodromy Dependence and Connection Formulae For Isomonodromic Tau Functions”, Duke Math. J., 167:7 (2018), 1347–1432  crossref  mathscinet  zmath  isi  scopus
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