arXiv subjects
Publications and source records attributed to R. R. Gontsov.
We study some properties of tau-functions of an isomonodromic deformation leading to the fifth Painlevé equation. In particular, here is given an elementary proof of Miwa's formula for the logarithmic differential of a tau-function.
We propose an analytic proof of the Malgrange-Sibuya theorem concerning a sufficient condition of the convergence of a formal power series satisfying an ordinary differential equation. The proof is based on the majorant method and allows to estimate the radius of convergence of such a series.
We obtain some sufficient conditions for reducibility of a Schlesinger isomonodromic family with the (block) upper-triangular monodromy to the same (block) upper-triangular form via a constant gauge transformation. We also obtain integral representations of hypergeometric type for entries of upper-triangular solutions of the Schlesinger equation.
We study movable singularities of Garnier systems using the connection of the latter with Schlesinger isomonodromic deformations of Fuchsian systems
We study movable singularities of Garnier systems 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.
We give some additions to the article "On the generalized Riemann-Hilbert problem with irregular singularities" by Bolibruch, Malek, Mitschi (math/0410483). In particular, a weak GRH-problem and the GRH-problem for scalar differential equations are discussed.