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Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components
Abstract
We construct examples of uniformly quasiregular mappings (uqr) acting on a sphere and having Fatou set consisting of infinitely many components. In particular we construct a uqr mapping providing a higher dimensional counterpart for the polynomial z ↦ z2 − 1 acting on the extended complex plane ℂ̂.
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BibTeX
@misc{martin2026examples,
title = {{Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components}},
author = {Gaven Martin and Kirsi Peltonen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.27746},
eprint = {2606.27746},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.27746},
}
RIS
TY - UNPB
TI - Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components
AU - Gaven Martin
AU - Kirsi Peltonen
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2606.27746
UR - https://arxiv.org/abs/2606.27746
AB - We construct examples of uniformly quasiregular mappings (uqr) acting on a sphere and having Fatou set consisting of infinitely many components. In particular we construct a uqr mapping providing a higher dimensional counterpart for the polynomial z ↦ z^2 − 1 acting on the extended complex plane ℂ̂.
ER -