On sufficient conditions for the existence of a Fuchsian equation with prescribed monodromy
type: Item
instance of: scholarly article
title: On sufficient conditions for the existence of a Fuchsian equation with prescribed monodromy
zbMATH Open document ID: 0952.34073
DOI: 10.1023/A:1021735104618
author: A. A. Bolibrukh
published in: Journal of Dynamical and Control Systems
publication date: 2000-04-13T00:00:00Z
review text: The paper offers an excellent review of some known results regarding sufficient conditions for positive solvability of the Riemann-Hilbert problem. It then goes into some new results regarding the solvability of the problem. The paper addresses the Riemann-Hilbert problem for a certain class of linear ordinary differential equations in the complex domain. The system \[ {dy\over dz}= B(z)y \] with unknown vector-valued function, \(y= (y',\dots, y^p)^t\), (where \(t\) is transposition), has singularities at \(a_1,\dots, a_n\). That is to say \(B(z)dz\) is holomorphic in \(\mathbb{C}\setminus\{a_1,\dots, a_n\}\) and \(\mathbb{C}\) is the Riemann sphere. Should the \(a_i\) be a pole of order one the system is said to be Fuchsian. Then the 21st Hilbert problem for Fuchsian linear systems is formulated and very well treated in the paper. Several excellent results are obtained regarding the form of all the monodromy matrices for the problem.
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 14D99
zbMATH DE Number: 1431889
zbMATH Keywords: monodromy
zbMATH Keywords: Fuchsian system
zbMATH Keywords: vector bundle
zbMATH Keywords: semistability
zbMATH Keywords: positive solvability
zbMATH Keywords: Riemann-Hilbert problem
reviewed by: John Schmeelk
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1431889