R. R. Gontsov

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We study movable singularities of Garnier systems (and Painlevé VI equations) using the connection of the latter with isomonodromic deformations of Fuchsian systems. Questions on the existence of solutions for some inverse monodromy problems are also considered. In the middle of the XIXth century B. Riemann [28] considered the problem of the construction of(More)
We study movable singularities of Garnier systems using the connection of the latter with Schlesinger isomonodromic deformations of Fuchsian systems. §1. What is Painlevé VI equations and Garnier systems? We start with the Painlevé VI (P VI) equation d 2 u dt 2 = 1 2 1 u + 1 u − 1 + 1 u − t du dt 2 − 1 t + 1 t − 1 + 1 u − t du dt + + u(u − 1)(u − t) t 2 (t(More)
We consider the generalized Riemann-Hilbert problem for linear differential equations with irregular singularities. After recalling the formulation of the problem in terms of vector bundles over the Riemann sphere, we give some estimates for the unique non-minimal Poincaré rank of the system and the number of apparent singularities of the scalar equation(More)
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