Alastair N. Fletcher

activity

20182026

collaborators

11 papers

math.DS2026

Cantor's onion: a uniformly quasiregular map whose Julia set is a Cantor set of spheres

Alastair N. Fletcher, Gaven J. Martin

For integers $d, m \geq 2$ with $1/ d + 1/ m < 1$ , we construct a uniformly quasiregular map of $S^{3}$ of degree $d^{2} + m^{2}$ whose Julia set is a Cantor set of concentric round spheres…

math.DS2026

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 $R^{n}$ , $n \geq 2$ : either all orbits are relatively compact, or the iterates conver…

math.DS2026

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…

math.DS2026

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…

math.DS2026

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.

math.CV2025

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…

math.CV2025

Geometric Function Theory on Uniformly Quasiconformally Homogeneous Domains

Alastair Fletcher, Allyson Hahn

Uniformly quasiconformally homogeneous domains in $R^{n}$ carry a transitive collection of $K$ -quasiconformal maps for a fixed $K \geq 1.$ In this paper, we study two questio…

math.CV2024

Interpolating quasiregular power mappings

Jack Burkart, Alastair N. Fletcher, Daniel A. Nicks

We construct a quasiregular mapping in $R^{3}$ that is the first to illustrate several important dynamical properties: the quasi-Fatou set contains wandering components; the…

math.DS2024

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…

math.CV2018

Attractor sets and Julia sets in low dimensions

A. Fletcher

If $X$ is the attractor set of a conformal IFS in dimension two or three, we prove that there exists a quasiregular semigroup $G$ with Julia set equal to $X$ . We also show that in…

math.DS2018

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…