17 citations · 69 across the 12 of their papers we have counts for
4 papers · 1 filter
The MacLane class and the Eremenko-Lyubich class
Karl F. Barth, Philip J. Rippon, David J. Sixsmith
In 1970 G. R. MacLane asked if it is possible for a locally univalent function in the class to have an arc tract. This question remains open, but several results abou…
The dynamics of quasiregular maps of punctured space
Daniel A. Nicks, David J. Sixsmith
The Fatou-Julia iteration theory of rational and transcendental entire functions has recently been extended to quasiregular maps in more than two real dimensions. Our goal in this…
Escaping sets of continuous functions
Ian Short, David J. Sixsmith
Our objective is to determine which subsets of arise as escaping sets of continuous functions from to itself. We obtain partial answers to this proble…
The size and topology of quasi-Fatou components of quasiregular maps
Daniel A. Nicks, David J. Sixsmith
We consider the iteration of quasiregular maps of transcendental type from to . In particular we study quasi-Fatou components, which are defined as the…