Daniel A. Nicks

activity

20092022

most citedQuasiregular dynamics on the n-sphere

5 citations · 6 across the 4 of their papers we have counts for

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4 papers · 1 filter

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

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

We show that for many families of transcendental entire functions $f$ the property that $m^{n} (r) \to \infty$ as $n \to \infty$ , for some $r > 0$ , where $m (r) = min {∣ f (z) ∣ : ∣ z ∣ = r}$ , impli…

math.DS2018

The bungee set in quasiregular dynamics

Daniel A. Nicks, David J. Sixsmith

In complex dynamics, the bungee set is defined as the set points whose orbit is neither bounded nor tends to infinity. In this paper we study, for the first time, the bungee set of…

math.DS2012

Chaotic dynamics of a quasiregular sine mapping

Alastair N. Fletcher, Daniel A. Nicks

This article studies the iterative behaviour of a quasiregular mapping S:\R^d\to\R^d that is an analogue of a sine function. We prove that the periodic points of S form a dense sub…