Hollow quasi-Fatou components of quasiregular maps
Nicks, Daniel A. and Sixsmith, David J. (2017) Hollow quasi-Fatou components of quasiregular maps. Mathematical Proceedings of the Cambridge Philosophical Society, 162 (3). pp. 561-574. ISSN 1469-8064
Official URL: https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/hollow-quasi-fatou-components-of-quasiregular-maps/B8F599AA67A1CCA4FB4D5CDE988AAC16
We define a quasi-Fatou component of a quasiregular map as a connected component of the complement of the Julia set. A domain in Rd is called hollow if it has a bounded complementary component. We show that for each d≥2 there exists a quasiregular map of transcendental type f:Rd→Rd with a quasi-Fatou component which is hollow.
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