Stokes phenomenon for single-level linear differential systems: a perturbative approach

Pascal Remy (1)

1 Chercheur indépendant

Given a meromorphic linear differential system with an arbitrary single level $r \geq 1$, we build a regular holomorphic perturbation which preserves the single level and we show that the Stokes-Ramis matrices of the initial system are limits of convenient products of the perturbed one. As an application, we provide an alternative method for the effective calculation of the Stokes multipliers of the initial system illustrated on two examples. No assumption of genericity is made on the initial system.

Mots clés: Linear differential system; regular perturbation; holomorphic perturbation; Stokes phenomenon; summability; Stokes multipliers

Domaines: Systèmes dynamiques [math.DS]

Pascal Remy. Stokes phenomenon for single-level linear differential systems: a perturbative approach. Funkcialaj ekvacioj.Serio internacia, 2015, 58, pp.172-222. ⟨hal-00795168⟩