## Departmental PhD Thesis Exam – Jonguk Yang

Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

Wednesday, May 17, 2017
11:10 a.m.
BA6183

PhD Candidate:  Jonguk Yang
Supervisor:  Michael Yampolsky
Thesis title:  Applications of Renormalization in Irrationally Indifferent Complex Dynamics

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Abstract:

This thesis comprises of two main results which are proved using renormalization techniques.

For the first result, we show that a quadratic polynomial with a fixed Siegel disc of bounded type rotation number is conformally mateable with the basilica polynomial $f_B(z) := z^2-1$.

For the second result, we study sufficiently dissipative complex quadratic Hénon maps with a semi-Siegel fixed point of inverse golden-mean rotation number. It was recently shown by Gaidashev, Radu and Yampolsky that the Siegel disks of such maps are bounded by topological circles. We investigate the geometric properties of such curves, and demonstrate that they cannot be $C^1$-smooth.

A copy of the thesis can be found here: Jonguk Yang – Thesis Draft