8 papers
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.
On cubic Blaschke products
Alastair N. Fletcher, Alexandra Hill
We show that every cubic Blaschke product has a unique hyperbolic inflection point in the unit disk and, moreover, this point lies at the hyperbolic midpoint of the two critical po…
Geometric Function Theory on Uniformly Quasiconformally Homogeneous Domains
Alastair Fletcher, Allyson Hahn
Uniformly quasiconformally homogeneous domains in carry a transitive collection of -quasiconformal maps for a fixed In this paper, we study two questio…
Interpolating quasiregular power mappings
Jack Burkart, Alastair N. Fletcher, Daniel A. Nicks
We construct a quasiregular mapping in that is the first to illustrate several important dynamical properties: the quasi-Fatou set contains wandering components; the…
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…