Logarithmic singularities of Fuchs equations, and a criterion for the monodromy group to be finite
type: Item
instance of: scholarly article
title: Logarithmic singularities of Fuchs equations, and a criterion for the monodromy group to be finite
zbMATH Open document ID: 0549.34005
DOI: 10.1007/BF01157466
published in: Mathematical Notes
publication date: 1983-01-01T00:00:00Z
review text: Consider the linear differential equation (*) \(y^{(n)}+a_ 1(x)y^{(n-1)}+...+a_ n(x)y=0\), where the coefficients \(a_ 1,...,a_ n\) are complex rational functions. The author considers two basic questions regarding (*). First, under what conditions are logarithmic terms absent from the asymptotic expansion of a solution in the neighborhood of a singular point? And second, when is the monodromy group of (*) finite? Both questions are reformulated in terms of appropriate properties of the Hall group associated with (*).
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A25
zbMATH DE Number: 3875711
zbMATH Keywords: logarithmic singularity
zbMATH Keywords: Fuchsian equation
zbMATH Keywords: singular point
zbMATH Keywords: monodromy group
zbMATH Keywords: Hall group
author: Mykola Grygorenko
MaRDI profile type: Publication
cites work: Logarithmic solutions of linear differential systems with a singularity of the first kind† ‡
cites work: Q4116553
cites work: On Second Order Linear Differential Equations with Algebraic Solutions on Algebraic Curves
cites work: Q3872768
description: scientific article; zbMATH DE number 3875711