4 papers · 1 filter
Uniform bounds for bubbles of neutral quadratic polynomials
Dzmitry Dudko, Willie Rush Lim
Given a quadratic polynomial with an irrationally indifferent fixed point of bounded type, a bubble is an iterated preimage of its Siegel disk. Similar to pseudo-Siegel disks, one…
The combinatorics of sector renormalization
Willie Rush Lim
The goal of this note is to systematically develop the fundamental arithmetic and combinatorial properties of the sector renormalization operation on rigid rotations. We employ the…
Hyperbolicity of renormalization of critical quasicircle maps
Willie Rush Lim
There is a well developed renormalization theory of real analytic critical circle maps by de Faria, de Melo, and Yampolsky. In this paper, we extend Yampolsky's result on hyperboli…
Rigidity of J-rotational rational maps and critical quasicircle maps
Willie Rush Lim
We present a number of rigidity results concerning holomorphic dynamical systems admitting rotation quasicircles. Firstly, we show the absence of line fields on the Julia set of an…