Stokes versus resurgence multipliers for ordinary linear di¤erential systems with a single arbitrary level

We provide a proof of the summability-resurgence of solutions of any ordinary linear di¤erential system with a single arbitrary level r following Ecalles method by regular per-turbation and majorant series. We deduce from it a precise description of singularities in the Borel plane with an application to the exact correspondence between resurgence multipliers (or connection constants) in the Borel plane and Stokes multipliers in the Laplace plane.