Parameter spaces in complex dynamics and related topics

Rigidity of Bounded-type Siegel Polynomials

speaker: Kostiantyn Drach (Universitat de Barcelona)

abstract: In this talk, we will discuss bounded-type Siegel polynomials, which are complex polynomials of arbitrary degree that contain a Siegel disk with a bounded-type rotation number. We will outline the proof of the result stating that non-renormalizable bounded-type Siegel polynomials are quasi-conformally rigid, and under certain natural assumptions, they are even conformally rigid. This means that any topological conjugacy between a pair of such polynomials is automatically quasi-conformalconformal. This theorem extends the existing results on rigidity for non-renormalizable polynomials of arbitrary degree by incorporating irrational neutral dynamics. This work is based on joint research with Jonguk Yang.

timetable:
Tue 28 May, 14:30 - 15:20, Aula Dini
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