Nouveaux résultats autour des formes super-irréductibles d’un système différentiel linéaire

摘要

In this paper we define canonical forms of the matrix M of the linear differential equation $ (S) : frac{dY}{dx} = MY $, such that the Newton polygon of the characteristic polynom of M is equal to the Newton polygon of (S), and we use super-irreducible forms to introduce two invariant polygons: the upper and the lower Newton Polygon. We prove that the Newton polygon of the characteristic polynomial of a super-irreducible form is equal to the Newton polygon, and use a “partially super-irreducible matrix” to compute the exponential part of formal solutions.