Geometry of Feigenbaum Julia sets
speaker: Misha Lyubich (Stony Brook University)abstract: Feigenbaum quadratic maps appear naturally through cascades of bifurcations of attracting cycles. Properties of their Julia sets J are quite fascinating and intimately related to the Universality and Rigidity phenomena in geometry and dynamics. We consider the following Basic Trichotomy for these sets:
1) Lean case: HD(J)< 2;
2) Balanced case: HD(J)=2 but area(J)=0;
3) Black Hole case: area(J)>0.
We show that all three options are realizable in the Feigenbaum class. In particuar, this provides us with ``tame" and ``observable" Julia sets of positive area (with explicit topological models and computable images).
Existence of such Julia sets goes against intuition coming from hyperbolic geometry and theory of Kleinian groups.
It is a joint work with Artur Avila.
timetable:
Wed 16 Oct, 9:00 - 10:00, Aula Dini
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