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arXiv · 2606.27746

Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components

Gaven Martin·Kirsi Peltonen
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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 $z \mapsto z^2 - 1$ acting on the extended complex plane $\hat{\mathbb{C}}$.

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Gaven Martin, Kirsi Peltonen. 2026-06-26. Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components. https://arxiv.org/abs/2606.27746

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