On polynomial asymptotics and Ramis-Sibuya Theorem.
Abstract: In a joint paper with M. Canalis-Durand and R. SchÄafke, a notion of monomial asymptotics was introduced, in order to study doubly singular dfferential equations, i.e., singularly perturbed differential equations with a singularity in the parameter, and an irregular singularity in the variable.
In this talk, we propose a generalization of this notion, defining polynomial asymptotics in two variables. For this aim we use the reduction of the singularities of plane curves in order to reduce the polynomial to a normal crossing situation, where monomial asymptotics in applicable. Using reduction of singularities and cohomological arguments, we can prove a theorem of Ramis-Sibuya type suitable for this class of asymptotics.
It is a joint work with Reinhard Schäfke (Université de Strasbourg).
Varsovia, Polonia. 10 al 13 de Septiembre de 2012.