On the Stokes phenomenon of a family of multi-perturbed level-one meromorphic linear differential systems

Pascal Remy (1)

1 Chercheur indépendant

Given a level-one meromorphic linear differential system, we are interested in the behavior of its Stokes-Ramis matrices under the action of a holomorphic perturbation acting on the non-zero Stokes values. In particular, we show that the Stokes-Ramis matrices of the given system can be expressed as limit of convenient connection matrices of the perturbed systems. We believe that this result could provide an efficient tool for the numerical calculation of the Stokes-Ramis matrices. No assumption of genericity is made.

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

Domaines: Systèmes dynamiques [math.DS]

Pascal Remy. On the Stokes phenomenon of a family of multi-perturbed level-one meromorphic linear differential systems. Journal of Dynamical and Control Systems, 2013, 19 (4), pp.575-592. ⟨10.1007/s10883-013-9196-1⟩. ⟨hal-00707031v2⟩