Multi-resurgence of formal solutions of linear meromorphic differential systems

Pascal Remy (1)

1 Chercheur indépendant

In this paper, we consider a linear meromorphic differential system at the origin. For any of its levels $\rho$, we prove with the factorization theorem that the Borel transforms of its $\rho$-reduced formal solutions are resurgent and we give a complete description of all their singularities. Then, restricting ourselves to some special geometric configurations of the singular points of these Borel transforms, we make explicit formulae relating the Stokes multipliers of level $\rho$ of the given system to some connection constants in the Borel plane. So, we generalize the results already obtained by M. Loday-Richaud and the author for systems with a unique level and for the lowest and highest levels of systems with multi-levels. As an illustration, we develop one example.

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

Domaines: Systèmes dynamiques [math.DS]

Pascal Remy. Multi-resurgence of formal solutions of linear meromorphic differential systems. 2015. ⟨hal-01140091⟩