Resurgence and highest level’s connection-to-Stokes formulæ for some linear meromorphic differential systems

Singular Perturbation of Nonlinear Systems with Regular Singularity

“…Contrarily to the previous case ( = 0), the unique formal power series solution̂( , ) is always 1-summable, irrespective of whether (4), the additional condition satisfied by the eingenvalues of (0, 0), holds or not. The case of = −1, on the other hand, has been studied in [4] for ] = 1 and the summability of the formal series can be read from the properties of the initial data of (5). The case = 0 separates the two cases and we refer to [3] for an explanation on summability properties for each of distinct cases of simple examples in which and = ( ) are a scalar and a scalar function depending only on .…”

“…The case = 0 separates the two cases and we refer to [3] for an explanation on summability properties for each of distinct cases of simple examples in which and = ( ) are a scalar and a scalar function depending only on . For recent investigations of the linear meromorphic system (5) with ≥ 1, ( = 0) ̸ = 0, and ≡ 0, about summable-resurgent of the Borel transform of its highest level's reduced formal solutions and connectionto-Stokes formulas, see [5] and references therein.…”