Topological and Combinatorial Problems in One-dimensional Complex Dynamics

Satellite renormalization for complex quadratic polynomials

speaker: Mitsuhiro Shishikura (Kyoto University)

abstract: The renormalization has been one of the main focus of the theory of one-dimensional complex dynamics. It is connected to the conjectures of on the density of hyperbolicity and the local connectivity of the Mandelbrot set. For quadratic polynomials, there are two different types of renormalizations -- primitive and satellite. The primitive renormalizations has been successfully studied by Kahn and Lyubich and now there are powerful a priori bounds. The satellite type has a very different nature and our knowledge is limited. In this talk, we discuss the difference between two types of renormalizations and explain recent results on the satellite renormalizations.

timetable:
Mon 14 Oct, 10:00 - 11:00, Aula Dini
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