Zobrazeno 1 - 10
of 133
pro vyhledávání: '"Fletcher, Alastair"'
In this paper, we construct a quasiregular mapping $f$ in $\mathbb{R}^3$ that is the first to illustrate several important properties: the quasi-Fatou set contains bounded, hollow components, the Julia set contains bounded components and, moreover, s
Externí odkaz:
http://arxiv.org/abs/2411.10190
Autor:
Broderius, Mark, Fletcher, Alastair
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 for planar quasiregular mappings of degree two and constant complex d
Externí odkaz:
http://arxiv.org/abs/2408.11256
In this paper, we give for the first time a systematic study of the variance of the distance to the boundary for arbitrary bounded convex domains in $\mathbb{R}^2$ and $\mathbb{R}^3$. In dimension two, we show that this function is strictly convex, w
Externí odkaz:
http://arxiv.org/abs/2407.12041
We generalize the classical K\"onig's and B\"ottcher's Theorems in complex dynamics to certain quasiregular mappings in the plane. Our approach to these results is unified in the sense that it does not depend on the local injectivity, or not, of the
Externí odkaz:
http://arxiv.org/abs/2308.08668
We show that the set of Julia limiting directions of a transcendental-type $K$-quasiregular mapping $f:\mathbb{R}^n\to \mathbb{R}^n$ must contain a component of a certain size, depending on the dimension $n$, the maximal dilatation $K$, and the order
Externí odkaz:
http://arxiv.org/abs/2303.17053
The primary aim of this paper is to give topological obstructions to Cantor sets in $\mathbb{R}^3$ being Julia sets of uniformly quasiregular mappings. Our main tool is the genus of a Cantor set. We give a new construction of a genus $g$ Cantor set,
Externí odkaz:
http://arxiv.org/abs/2210.06619
Beardon and Minda gave a characterization of normal families of holomorphic and meromorphic functions in terms of a locally uniform Lipschitz condition. Here, we generalize this viewpoint to families of mappings in higher dimensions that are locally
Externí odkaz:
http://arxiv.org/abs/2201.08921
Autor:
Fletcher, Alastair, Pratscher, Jacob
We study the mean radius growth function for quasiconformal mappings. We give a new sub-class of quasiconformal mappings in $\mathbb{R}^n$, for $n\geq 2$, called bounded integrable parameterization mappings, or BIP maps for short. These have the prop
Externí odkaz:
http://arxiv.org/abs/2201.03037
Autor:
Fletcher, Alastair N., Vellis, Vyron
The Decomposition Problem in the class $LIP(\mathbb{S}^2)$ is to decompose any bi-Lipschitz map $f:\mathbb{S}^2 \to \mathbb{S}^2$ as a composition of finitely many maps of arbitrarily small isometric distortion. In this paper, we construct a decompos
Externí odkaz:
http://arxiv.org/abs/2106.00054
Autor:
Fletcher, Alastair N., Stoertz, Daniel
Publikováno v:
Pacific J. Math. 321 (2022) 283-307
We construct a geometrically self-similar Cantor set $X$ of genus $2$ in $\mathbb{R}^3$. This construction is the first for which the local genus is shown to be $2$ at every point of $X$. As an application, we construct, also for the first time, a un
Externí odkaz:
http://arxiv.org/abs/2009.12427