5 papers · 2 filters
Cantor's onion: a uniformly quasiregular map whose Julia set is a Cantor set of spheres
Alastair N. Fletcher, Gaven J. Martin
For integers with , we construct a uniformly quasiregular map of of degree whose Julia set is a Cantor set of concentric round spheres…
Schwarz-Pick and Denjoy-Wolff for uniformly quasiregular maps
Alastair N. Fletcher
We prove a Denjoy-Wolff theorem for uniformly quasiregular self-maps of the unit ball in , : either all orbits are relatively compact, or the iterates conver…
Equipotentials and folds for quasiregular Mandelbrot sets
Alastair N. Fletcher
It is well-known that Douady and Hubbard proved that the Mandelbrot set is connected by constructing a uniformizing holomorphic map for its complement from the Böttcher coordinates…
Sobolev mixing constants and compactness in rational moduli space
Alastair Fletcher, Ilya Krishtal
We study uniformity of Sobolev mixing estimates for rational maps and uniformly quasiregular mappings. For rational maps of fixed degree, the optimal centered Sobolev trace constan…
On the ternary Cantor set and Julia sets
A. N. Fletcher
In this article, we show that the ternary Cantor set is not the Julia set of a rational map.