Smallness of the formal exponents of an irregular linear differential system, with an application to solvability by quadratures.

par Moulay Barkatou

jeudi 25 oct. 2018, 10:30 → 11:30 Europe/Paris

Salle XR203 (Bâtiment XLIM)

 In this talk, I will  present a  recent joint work with Renat Gontsov (Russian Academy of Sciences).

We prove that the formal exponents of a linear differential system with non-resonant irregular singular points whose coefficient matrix is small, are also small enough. This implies that such a system is solvable by quadratures if, and only if its coefficient matrix is conjugated to a triangular one (via a constant conjugating matrix). This generalizes the corresponding theorem by Ilyashenko-Khovanskii for Fuchsian systems.