On the highest level's Stokes phenomenon of meromorphic linear differential systems
Résumé
Given a meromorphic linear differential system with several levels, we prove that the Borel transforms of its highest level's reduced formal solutions are summable-resurgent and we give a complete description of all their singularities. Then, as an application and under some convenient hypothesis on the geometric configuration of singular points, we state formulae to express some highest level's Stokes multipliers of the initial system in terms of connection constants in the Borel plane, generalizing thus formulae already displayed by M. Loday-Richaud and the author for systems with a single level. As an illustration, we develop three examples.
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