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- Daniel A. Nicks
- 2016

This article concerns the iteration of quasiregular mappings on $$\mathbb {R}^d$$Rd and entire functions on $$\mathbb {C}$$C. It is shown that there are always points at which the iterates of a… (More)

We define a quasi-Fatou component of a quasiregular map as a connected component of the complement of the Julia set. A domain in R is called hollow if it has a bounded complementary component. We… (More)

In this article, we investigate the boundary of the escaping set I(f) for quasiregular mappings on R, both in the uniformly quasiregular case and in the polynomial type case. The aim is to show that… (More)

It is well-known that the Julia set J(f) of a rational map f : C → C is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus, with the bound depending only on f . In… (More)

The Fatou-Julia iteration theory of rational functions has been extended to uniformly quasiregular mappings in higher dimension by various authors, and recently some results of Fatou-Julia type have… (More)

Baker's conjecture states that a transcendental entire function of order less than $1/2$ has no unbounded Fatou components. It is known that, for such functions, there are no unbounded periodic Fatou… (More)

- Daniel A. Nicks
- 2013

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 a quasiregular map… (More)