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Stabilizing differential operators. A method for computing invariants at irregular singularities. (English) Zbl 0746.34012
Differential equations and computer algebra, Proc. Workshop, Ithaca/NY (USA) 1990, 181-228 (1991).
This paper is concerned with algorithms related to singularities of systems of first order homogeneous linear differential equations with complex analytic coefficients \[ dy_ i/dx+\sum^ n_{j=1} a_{ij} y_ j=0\text{ for } i\in\{1,\dots,n\}.\tag{1} \] Here \(x_ 0\) is a singularity of (1) if \(x_ 0\) is a singular point of some \(a_{ij}\) (only poles are admitted). The author is, in particular, interested in formal solutions of (1). Moreover, his study is ‘local’. The method of this paper gives another look on the so-called super-irreducible forms of systems like (1) as defined and studied by A. Hilali and A. Wasner [Numer. Math. 50, 429-449 (1987; Zbl 0627.65091)].

MSC:
34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
34A30 Linear ordinary differential equations and systems, general