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)
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.
scientific article; zbMATH DE number 4004636
scientific article