1 citations · 2 across the 4 of their papers we have counts for
7 papers
Rigidity of the attractor of neutral renormalization
Dzmitry Dudko, Willie Rush Lim, Mikhail Lyubich
We prove combinatorial rigidity for the full renormalization attractor of neutral quadratic polynomials. More precisely, any two bi-infinite renormalization towers with the same co…
Lebesgue measure of the postcritical set of neutral quadratic polynomials
Willie Rush Lim
We prove that the postcritical set of every quadratic polynomial with a neutral fixed point has zero Lebesgue measure. In particular, no arithmetic condition on the rotation number…
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 paper is to systematically develop the fundamental arithmetic and combinatorial properties of the sector renormalization operation on rigid rotations. We employ th…
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…
A priori bounds and degeneration of Herman rings with bounded type rotation number
Willie Rush Lim
By adapting the near-degenerate regime designed by Kahn, Lyubich, and D. Dudko, we prove that the boundaries of Herman rings with bounded type rotation number and of the simplest c…