7 papers · 1 filter
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.
An analogue of Green's Functions for Quasiregular Maps
Mark Broderius, Alastair Fletcher
Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions…
Quasiregular semigroups with examples
A. Fletcher
Rational semigroups were introduced by Hinkkanen and Martin as a generalization of the iteration of a single rational map. There has subsequently been much interest in the study of…