Q1089482
type: Item
instance of: scholarly article
title: Calcul des invariants de Malgrange et de Gérard-Levelt d'un système différentiel linéaire en un point singulier irrégulier. (The Malgrange and Gérard-Levelt invariants calculus of a differential system linear in an irregular singular point)
zbMATH Open document ID: 0619.34009
DOI: 10.1016/0022-0396(87)90126-4
author: B. George
published in: Journal of Differential Equations
publication date: 1987-01-01T00:00:00Z
review text: We consider a system of ordinary differential equations (\(\Delta)\) \(Y'(x)=A(x)Y(x)\), where A(x) is a matrix with a pole of the order q at \(x=0\). For this system, B. Malgrange has introduced the quantity i(D), which can be computed with the cyclic vector method. The present paper treats the practical evaluation of i(D) and the invariants \(\rho_ 1,\rho_ 2,...,\rho_{q-1}\), of Gérard and Levelt without using a cyclic vector. First, we give a survey of the algorithm given by the author and \textit{A. Wazner} [Numer. Math. 50, 429-449 (1987)] by which a system (\(\Delta)\) is reduced to a super-irreducible form. We show that these invariants follow directly from this form.
Mathematics Subject Classification ID: 34M99
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 4004636
zbMATH Keywords: first order differential equation
zbMATH Keywords: cyclic vector method
zbMATH Keywords: super- irreducible form
MaRDI profile type: Publication
full work available at URL: 0022-0396(87)90126-4
OpenAlex ID: W2061927401
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label: Calcul des invariants de Malgrange et de Gérard-Levelt d'un système différentiel linéaire en un point singulier irrégulier. (The Malgrange and Gérard-Levelt invariants calculus of a differential system linear in an irregular singular point)
description: scientific article; zbMATH DE number 4004636