The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces

Mathematics – Classical Analysis and ODEs

Scientific paper

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18 pages, an additional section is added

Scientific paper

Some representation of a pair "a bundle with a connection" on a Riemann surface, based on a representation of a surface as a factor of an exterior of a unit disk, is introduced. In this representation isomonodromic deformations of bundles with logarithmic connections are described by some modification of the Schlesinger system on a Riemann sphere (typically this modification is just the ordinary Schlesinger system) plus some linear system.

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