The fixed point of parabolic renormalization

The fixed point of parabolic renormalization

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Michael Yampolsky , Univeristy of Toronto
Fine Hall 801

Please note special day (Tuesday). I will present our joint work with O. Lanford on the parabolic renormalization operator acting on the space of simple parabolic analytic germs. We have constructed a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties.This class contains the Inou-Shishikura renormalization fixed point. I will also discuss an approach to numerical computation of the renormalization fixed point map based on an asymptotic expansion for the Fatou coordinate, which is resurgent in the sense of J. Ecalle.