Stokes-Ramis matrices and connection constants for meromorphic linear differential systems with a single level: a perturbative approach.

Pascal Remy (1)

1 Chercheur indépendant

In the article Matrices de Stokes-Ramis et constantes de connexion pour les systèmes différentiels linéaires de niveau unique (P. Remy), we considered linear differential systems with a unique but arbitrary level and we stated formulae to express all the Stokes multipliers in terms of connection constants in the Borel plane generalizing thus the calculations made in the article Resurgence, Stokes phenomenon and alien derivatives for level-one linear differential systems (M. Loday-Richaud, P. Remy). In the present paper, we provide a new proof of these formulae. We perturb the given system in order that each Stokes value generate its own anti-Stokes direction. We state the connection-to-Stokes formulae for the perturbed system and we conclude by a limit process. We believe the method could provide an efficient tool for the numerical calculation of the Stokes multipliers. As an illustration, we develop an example. No assumption of genericity is made.

Mots clés: Linear differential system; Stokes phenomenon; summability; resurgence; Stokes multipliers; connection constants

Domaines: Systèmes dynamiques [math.DS]

Pascal Remy. Stokes-Ramis matrices and connection constants for meromorphic linear differential systems with a single level: a perturbative approach.. 2011. ⟨hal-00701738⟩