First level's connection-to-Stokes formulae for meromorphic linear differential systems

Pascal Remy (1)

1 Chercheur indépendant

Given a multi-leveled meromorphic linear differential system, we deduce from the factorization theorem explicit formulae allowing to express all the first level's Stokes multipliers in terms of connection constants in the Borel plane, generalizing thus the formulae displayed by M. Loday-Richaud and the author in the case of single-leveled systems. As an illustration, we develop three examples. 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. First level's connection-to-Stokes formulae for meromorphic linear differential systems. Advances in Dynamical Systems and Applications, 2012, 7 (2), pp.249-285. ⟨hal-00692093v2⟩