Parabolic renormalization

3 June 2013 - 7 June 2013

Aims

For analytic germs in one dimension with a simple parabolic point at the origin, the moduli space can be parametrized by pairs of parabolic germs using the so-called Ecalle-Voronin coefficients (i.e. the "horn maps"). Recently there was a lot of activity on parabolic renormalization, which maps a parabolic germ on one of the two parabolic germs of the associated pair and which is related to parabolic implosion, that is the study of the bifurcation appearing in family of germs containing a parabolic one. The aim is to confront geometric and analytical approaches to study the parabolic renormalization and to discuss what can be generalized to semi-parabolic and parabolic germs in higher dimension.