Geodesic
The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 370-386 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce a way to represent pairs $(E,\nabla)$, where $E$ is a bundle on a Riemann surface and $\nabla$ is a logarithmic connection in $E$, based on a representation of the surface as the quotient of the exterior of the unit disc. In this representation, we write the local isomonodromic deformation conditions for the pairs $(E,\nabla)$. These conditions are written as a modified Schlesinger system on a Riemann sphere (reduced to the ordinary Schlesinger system in the typical case) supplemented by a certain system of linear equations.
Mots-clés : isomonodromic deformation
Keywords: Riemann surface, Schlesinger system. 
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D. V. Artamonov. The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 3, pp. 370-386. http://geodesic.mathdoc.fr/item/TMF_2012_171_3_a1/

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