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Résumé |
I will give an introduction to transseries, resurgence and
generalized
Borel summability, from the point of view of Ecalle's theory, and their
extension to PDEs. I will also make the connection to hyperasymptotics
sometimes alternatively used in QFT and QCD and outline recent progresses.
As an application, I will discuss nonperturbative ionization of
Hydrogen atoms in periodic external fields and for which the survival
probability
has the surprising power law decay t^(-5/3). I will also speak about the
detailed
structure of Julia sets, as viewed using transseries. |
