seminar: Parabolic and near-parabolic renormalizations in complex dynamics

speaker: Hiroyuki Inou (Department of Mathematics, Kyoto University)

abstract: (Joint work with Mitsuhiro Shishikura) We introduce a new class of holomorphic germs of parabolic fixed point and show that it is invariant under parabolic renormalization and its perturbation (near-parabolic renormalization) with uniform contraction with respect to a certain metric. This helps us to analyze bifurcation phenomena of such a germ, which is closely related to delicate questions, e.g., linearizability problem, Cremer Julia sets and infinite satellite renormalizations. Buff and Chéritat used our result as one of the main tools in the construction of a quadratic polynomial with Julia set of positive Lebesgue measure.

timetable:
Thu 25 Jan, 9:00 - 10:00, Aula Dini
documents:

inou.pdf

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