Stokes operators via limit monodromy of generic perturbation
type: Item
instance of: scholarly article
title: Stokes operators via limit monodromy of generic perturbation
zbMATH Open document ID: 0949.34076
DOI: 10.1023/A:1021744801409
author: A. A. Glutsuk
published in: Journal of Dynamical and Control Systems
publication date: 2000-04-13T00:00:00Z
review text: The research of the behaviour of the solutions to linear differential equations in a neighbourhood of an irregular singular point represents considerable interest both from the theoretical and applied point of view. Recently the approach, in which the irregular singular point is represented as a limit of some set of regular singular points (so-called confluent singular points), has gained in increasing popularity [see \textit{A. Ronveaux}, Heun's differential equations, Oxford University Press (1995; Zbl 0847.34006)]. In the present paper the author proves, that if the irregular singular point of some linear differential equation is not resonant, then from the given equation it is possible by small deformation to receive a linear differential equation having only regular singular points and such, that the (matrix) operators of Stokes of an input equation are limiting values for matrices of transition between canonical bases in regular singular points of the perturbed equation.
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 34M40
zbMATH DE Number: 1431873
zbMATH Keywords: Stokes operators
zbMATH Keywords: limit monodromy
zbMATH Keywords: generic perturbation
zbMATH Keywords: solutions
zbMATH Keywords: linear differential equations
zbMATH Keywords: irregular singular point
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
full work available at URL: a:1021744801409
OpenAlex ID: W184627855
description: scientific article; zbMATH DE number 1431873