Daniel A. Nicks

activity

20092026

most citedFoundations for an iteration theory of entire quasiregular maps

16 citations · 81 across the 18 of their papers we have counts for

collaborators

21 papers

math.DS2026

Uniformly quasiregular maps of $R^{n}$ with Cantor Julia sets

Daniel A. Nicks

For any $n \geq 3$ , we construct uniformly quasiregular self-maps of $R^{n}$ of polynomial type for which the Julia set is a Cantor set.

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.CV2022

Normal families and quasiregular mappings

Alastair N. Fletcher, Daniel A. Nicks

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 vi…

math.CV2021

Iterating the minimum modulus: functions of order half, minimal type

Daniel A. Nicks, Philip J. Rippon, Gwyneth M. Stallard

For a transcendental entire function $f$ , the property that there exists $r > 0$ such that $m^{n} (r) \to \infty$ as $n \to \infty$ , where $m (r) = min {∣ f (z) ∣ : ∣ z ∣ = r}$ , is related to conjec…

math.DS2019

Which sequences are orbits?

Daniel A. Nicks, David J. Sixsmith

In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the func…

math.DS2018

Eremenko's conjecture for functions with real zeros: the role of the minimum modulus