All Outputs (3)

Hollow quasi-Fatou components of quasiregular maps (2016)
Journal Article
Nicks, D. A., & Sixsmith, D. J. (2017). Hollow quasi-Fatou components of quasiregular maps. Mathematical Proceedings, 162(3), https://doi.org/10.1017/S0305004116000840

We define a quasi-Fatou component of a quasiregular map as a connected component of the complement of the Julia set. A domain in Rd is called hollow if it has a bounded complementary component. We show that for each d≥2 there exists a quasiregular ma... Read More about Hollow quasi-Fatou components of quasiregular maps.

The size and topology of quasi-Fatou components of quasiregular maps (2016)
Journal Article
Nicks, D. A., & Sixsmith, D. J. (2017). The size and topology of quasi-Fatou components of quasiregular maps. Proceedings of the American Mathematical Society, 145(2), 749-763. https://doi.org/10.1090/proc/13253

We consider the iteration of quasiregular maps of transcendental type from Rd to Rd. In particular we study quasi-Fatou components, which are defined as the connected components of the complement of the Julia set. Many authors have studied the compon... Read More about The size and topology of quasi-Fatou components of quasiregular maps.

Slow escaping points of quasiregular mappings (2016)
Journal Article
Nicks, D. A. (in press). Slow escaping points of quasiregular mappings. Mathematische Zeitschrift, https://doi.org/10.1007/s00209-016-1687-9

This article concerns the iteration of quasiregular mappings on Rd and entire functions on C. It is shown that there are always points at which the iterates of a quasiregular map tend to infinity at a controlled rate. Moreover, an asymptotic rate of... Read More about Slow escaping points of quasiregular mappings.