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math.DS2026
On the ternary Cantor set and Julia sets
A. N. Fletcher
In this article, we show that the ternary Cantor set is not the Julia set of a rational map.
math.DS2024
Genus Cantor sets and germane Julia sets
Alastair N. Fletcher, Daniel Stoertz, Vyron Vellis
The primary aim of this paper is to give topological obstructions to Cantor sets in being Julia sets of uniformly quasiregular mappings. Our main tool is the genus o…
math.DS2024
Phragmén-Lindelöf Principles and Julia Limiting Directions of Quasiregular Mappings
Alastair N. Fletcher, Julie M. Steranka
We show that the set of Julia limiting directions of a transcendental-type -quasiregular mapping must contain a component of a certain size, dep…