Interpolating quasiregular power mappings
Complex Variables
2025-03-19 v2 Dynamical Systems
Abstract
We construct a quasiregular mapping in that is the first to illustrate several important dynamical properties: the quasi-Fatou set contains wandering components; these quasi-Fatou components are bounded and hollow; and the Julia set has components that are genuine round spheres. The key tool in this construction is a new quasiregular interpolation in round rings in between power mappings of differing degrees on the boundary components. We also exhibit the flexibility of constructions based on these interpolations by showing that we may obtain quasiregular mappings which grow as quickly, or as slowly, as desired.
Keywords
Cite
@article{arxiv.2411.10190,
title = {Interpolating quasiregular power mappings},
author = {Jack Burkart and Alastair N. Fletcher and Daniel A. Nicks},
journal= {arXiv preprint arXiv:2411.10190},
year = {2025}
}