|
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
Full text:
http://www.ams.org/.../abst2-4-2002.html
 References:
PDF file
HTML file
Bibliographic databases:
   
MSC: 14, 79
Received: February 18, 2002; in revised form April 20, 2002
Language:
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
\Bibitem{Kri02}
\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
\mathnet{http://mi.mathnet.ru/mmj70}
\crossref{https://doi.org/10.17323/1609-4514-2002-2-4-717-752}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1986088}
\zmath{https://zbmath.org/?q=an:1044.70010}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208593600005}
\elib{http://elibrary.ru/item.asp?id=8379141}
Linking options:
http://mi.mathnet.ru/eng/mmj70 http://mi.mathnet.ru/eng/mmj/v2/i4/p717
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
Grava T., “Whitham equations, Bergman kernel and Lax-Levermore minimizer”, Acta Appl. Math., 82:1 (2004), 1–86
 -
Pinchbeck D.J., “Isomonodromic flows for Fuchsian connections on Riemann surfaces”, Int. Math. Res. Not., 2005, no. 40, 2473–2497
-
Teodorescu R., “Relaxation of nonlinear oscillations in BCS superconductivity”, J. Phys. A, 39:33 (2006), 10363–10374
-
Fedorov R.M., “Algebraic and Hamiltonian approaches to isostokes deformations”, Transform. Groups, 11:2 (2006), 137–160
-
I. M. Krichever, O. K. Sheinman, “Lax Operator Algebras”, Funct. Anal. Appl., 41:4 (2007), 284–294
 -
Mazzocco M., Mo Man Yue, “The Hamiltonian structure of the second Painlevé hierarchy”, Nonlinearity, 20:12 (2007), 2845–2882
-
Boalch Ph., “Quasi-Hamiltonian geometry of meromorphic connections”, Duke Math. J., 139:2 (2007), 369–405
-
Dubrovin B., Mazzocco M., “Canonical structure and symmetries of the Schlesinger equations”, Comm. Math. Phys., 271:2 (2007), 289–373
-
M. Schlichenmaier, O. K. Sheinman, “Central extensions of Lax operator algebras”, Russian Math. Surveys, 63:4 (2008), 727–766
-
O. K. Sheinman, “Lax Operator Algebras and Integrable Hierarchies”, Proc. Steklov Inst. Math., 263 (2008), 204–213
-
Hurtubise J., “On the geometry of isomonodromic deformations”, J. Geom. Phys., 58:10 (2008), 1394–1406
-
Kokotov A., Korotkin D., “A new hierarchy of integrable systems associated to Hurwitz spaces”, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 366:1867 (2008), 1055–1088
-
Schlichenmaier M., “Classification of central extensions of Lax operator algebras”, Geometric Methods in Physics, AIP Conference Proceedings, 1079, 2008, 227–234
-
Dzhamay A., “Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painlevé equations”, J. Phys. A, 42:45 (2009), 454008, 10 pp.
-
Heu V., “Stability of rank 2 vector bundles along isomonodromic deformations”, Math. Ann., 344:2 (2009), 463–490
-
Heu V., “Universal Isomonodromic Deformations of Meromorphic Rank 2 Connections on Curves”, Ann Inst Fourier (Grenoble), 60:2 (2010), 515–549
-
Machu F.-X., “Local Structure of Moduli Spaces”, Internat J Math, 22:12 (2011), 1683–1709
-
Teschner J., “Quantization of the Hitchin Moduli Spaces, Liouville Theory and the Geometric Langlands Correspondence I”, Adv. Theor. Math. Phys., 15:2 (2011), 471–564
-
Yu. P. Bibilo, “Isomonodromic deformations of systems of linear differential equations with irregular singularities”, Sb. Math., 203:6 (2012), 826–843
-
D. V. Artamonov, “The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces”, Theoret. and Math. Phys., 171:3 (2012), 739–753
-
Zabrodin A., Zotov A., “Quantum Painlevé-Calogero Correspondence for Painlevé VI”, J. Math. Phys., 53:7 (2012), 073508
-
Wong M.L., “An Interpretation of Some Hitchin Hamiltonians in Terms of Isomonodromic Deformation”, J. Geom. Phys., 62:6 (2012), 1397–1413
-
Artamonov D.V., “Isomonodromic Deformations on Riemann Surfaces”, Painleve Equations and Related Topics (2012), Degruyter Proceedings in Mathematics, eds. Bruno A., Batkhin A., Walter de Gruyter & Co, 2012, 85–89
-
Wong M.L., “Hecke Modifications, Wonderful Compactifications and Moduli of Principal Bundles”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 12:2 (2013), 309–367
-
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118
-
M. Schlichenmaier, “Multipoint Lax operator algebras: almost-graded structure and central extensions”, Sb. Math., 205:5 (2014), 722–762
-
Boalch P.P., “Geometry and Braiding of Stokes Data; Fission and Wild Character Varieties”, Ann. Math., 179:1 (2014), 301–365
-
Boalch Ph., “Poisson Varieties From Riemann Surfaces”, Indag. Math.-New Ser., 25:5, SI (2014), 872–900
-
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
-
Trans. Moscow Math. Soc., 76:2 (2015), 219–236
-
Aminov G., Arthamonov S., “New -Matrix Linear Problems For the Painlevé Equations III, V”, Constr. Approx., 41:3, SI (2015), 357–383
-
Arata Komyo, “The Moduli Spaces of Parabolic Connections with a Quadratic Differential and Isomonodromic Deformations”, SIGMA, 14 (2018), 111, 22 pp.
-
Its A.R., Prokhorov A., “On Some Hamiltonian Properties of the Isomonodromic Tau Functions”, Rev. Math. Phys., 30:7, SI (2018), 1840008
 -
Its A.R., Lisovyy O., Prokhorov A., “Monodromy Dependence and Connection Formulae For Isomonodromic Tau Functions”, Duke Math. J., 167:7 (2018), 1347–1432
|
| Number of views: |
| This page: | 613 | | References: | 80 |
|
Terms of Use