From the 1 of 4 linked papers with an AI index.
4 papers
The combinatorics of sector renormalization
Willie Rush Lim
The paper develops the arithmetic and combinatorial structure of sector renormalization for rigid rotations using modified continued fractions, and shows how infinite return times…
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…
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…
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…