Interpolating quasiregular power mappings
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916655781642240 |
|---|---|
| author | Burkart, Jack Fletcher, Alastair N. Nicks, Daniel A. |
| author_facet | Burkart, Jack Fletcher, Alastair N. Nicks, Daniel A. |
| contents | We construct a quasiregular mapping in $\mathbb{R}^3$ 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 $\mathbb{R}^3$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10190 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interpolating quasiregular power mappings Burkart, Jack Fletcher, Alastair N. Nicks, Daniel A. Complex Variables Dynamical Systems We construct a quasiregular mapping in $\mathbb{R}^3$ 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 $\mathbb{R}^3$ 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. |
| title | Interpolating quasiregular power mappings |
| topic | Complex Variables Dynamical Systems |
| url | https://arxiv.org/abs/2411.10190 |