Classical Analysis

Seminar information archive ~06/24Next seminarFuture seminars 06/25~


16:45-18:15   Room #154 (Graduate School of Math. Sci. Bldg.)
David Sauzin (CNRS)
Introduction to resurgence on the example of saddle-node singularities (ENGLISH)
[ Abstract ]
Divergent power series naturally appear when solving such an elementary differential equation as x^2 dy = (x+y) dx, which is the simplest example of saddle-node singularity. I will discuss the formal classification of saddle-node singularities and illustrate on that case Ecalle's resurgence theory, which allows one to analyse the divergence of the formal solutions. One can also deal with resonant saddle-node singularities with one more dimension, a situation which covers the local study at infinity of some Painlevé equations.