Journal Article10.1134/S0081543811030035
Differential equations with meromorphic coefficients
A. A. Bolibrukh
- 14 Apr 2011
- Vol. 272, Iss: 2, pp 13-43
11
TL;DR: In this article, the following problems of the analytic theory of differential equations are considered: Hilbert's 21st problem for Fuchsian systems of linear differential equations, the Birkhoff normal form problem for systems of LDEs with irregular singularities, and the classification problem for isomonodromic deformations of Fuchsians.
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Abstract: The following problems of the analytic theory of differential equations are considered: Hilbert’s 21st problem for Fuchsian systems of linear differential equations, the Birkhoff normal form problem for systems of linear differential equations with irregular singularities, and the classification problem for isomonodromic deformations of Fuchsian systems.
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Citations
Construction of the Fuchs equation with four given finite critical points and a given reducible monodromy group in the resonance case
V. V. Amel’kin,M. N. Vasilevich +1 more
- 28 Jun 2019
TL;DR: In this paper, a reducible monodromy group of rank 2 on the complex projective line is constructed for the completely integrable Fuchs equation with four given finite critical points.
Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution
Yulia Bibilo,Galina Filipuk +1 more
TL;DR: In this article, it was shown that Bolibruch's non-Schlesinger deformations of resonant Fuchsian systems are, in general, not preserved by middle convolution.
Constructive Solutions to the Riemann---Hilbert Problem and Middle Convolution
Yulia Bibilo,Galina Filipuk +1 more
TL;DR: In this article, a general scheme to generate constructive solutions to the Riemann-Hilbert problem via middle convolution is presented. Butler et al. used a Fuchsian system with four singular points.
3
Middle convolution and non-Schlesinger deformations
Yulia Bibilo,Galina Filipuk +1 more
- 01 May 2015
1
Construction of a Fuchs Equation with Four Given Finite Singular Points and Given Reducible 2 × 2 Monodromy Matrices
V. V. Amel’kin,M. N. Vasilevich +1 more
TL;DR: On the complex projective line, the authors constructed a Fuchs equation with four given finite singular points and with fundamental solution matrix that has given reducible 2×2 monodromy matrices in the nonresonance case.
1
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