Seminari di Sistemi Dinamici e Olomorfi 2010-2011

seminar: Ecalle-Voronin invariants and resurgent functions

speaker: Artem Dudko (University of Stony Brook, Institute for Mathematical Sciences)

abstract: In this talk we will present Ecalle’s resurgence theory in application to dynamics of a simple parabolic germ $$f (z ) = z + z^2 + O(z^3)$$. By definition, Fatou coordinates are conformal solutions of the equation $$H(f (z )) = H(z ) + 1$$ in an attracting and a repelling Fatou petals. The Ecalle-Voronin invariants describe a relation between the Fatou coordinates and give a complete invariant of conformal conjugacy of simple parabolic germs. There is a formal solution H of the Fatou coordinate equation in terms of divergent series which gives an asymptotic expansion for the Fatou coordinates of f. The purpose of the talk is to present the "Bridge equation" which allows to recover Ecalle-Voronin invariants from H using Ecalle’s Alien Calculus. The work is in progress (joint with David Sauzin).

timetable:
Wed 4 May, 11:30 - 12:30, Sala Conferenze Centro De Giorgi
<< Go back