Project R-13160

Transseries and superexact asymptotics in ordinary and partial differential equations (Research)

The parallel development of transseries (Ecalle) and superexact asymptotics (Ilyashenko) in the nineties of the last century were proven successful in the study of so-called elementary polycycles. These polycycles (limit periodic sets of vector fields on an analytic surface) were the outcome of a desingularization process allowing one to reduce nilpotent singularities to a more elementary form. Looking beyond the question on polycycles, we make a comparison between the two techniques, combining benefits from both, and apply the refined methodology to questions concerning slow-fast systems, singular partial differential equations and o-minimal structures.

01 November 2022 - 31 October 2024