arXiv subjects
Publications and source records attributed to Jean-Marc Rasoamanana.
We consider the effective resummation of a Borel sum by its associated factorial series expansion. Our approach provides concrete estimates for the remainder term when truncating this factorial series. We then generalize a theorem of Nevanlinna which gives us the natural framework to extend the factorial series method for Borel-resummable fractional power series expansions.
In this article, we investigate the resurgent properties of the WKB solutions for a singularly perturbated second order ordinary differential equation. In particular, we extend and propose a new proof of a theorem due to Aoki (et al) near a simple turning point, in the framework of the exact WKB analysis. Our scheme of proof is based on a Laplace-integral representation derived from an existence theorem of holomorphic solutions for a linear singular partial differential equation.
We consider in the complex field the differential equation $\displaystyle \frac{d^2}{d x^2} Φ(x) = \frac{P_m(x,\a)}{x^2}Φ(x)$, where $P_m$ is a monic polynomial function of order $m$ with coefficients $\a=(a_1, ..., a_m)$. We investigate the asymptotic, resurgent, properties of the solutions at infinity, focusing in particular on the analytic dependence on $\a$ of the Stokes-Sibuya multipliers. Taking into account the non trivial monodromy at the origin, we derive a set of functional equations for the Stokes-Sibuya multipliers. We show how these functional relations can be used to compute the Stokes multipliers for a class of polynomials $P_m$. In particular, we obtain conditions for isomonodromic deformations when $m=3$.