The size and topology of quasiFatou components of quasiregular mapsTools Nicks, Daniel A. and Sixsmith, David J. (2017) The size and topology of quasiFatou components of quasiregular maps. Proceedings of the American Mathematical Society, 145 (2). pp. 749763. ISSN 10886826
AbstractWe consider the iteration of quasiregular maps of transcendental type from Rd to Rd. In particular we study quasiFatou components, which are defined as the connected components of the complement of the Julia set. Many authors have studied the components of the Fatou set of a transcendental entire function, and our goal in this paper is to generalise some of these results to quasiFatou components. First, we study the number of com plementary components of quasiFatou components, generalising, and slightly strengthening, a result of Kisaka and Shishikura. Second, we study the size of quasiFatou components that are bounded and have a bounded complementary component. We obtain results analogous to those of Zheng, and of Bergweiler, Rippon and Stallard. These are obtained using techniques which may be of interest even in the case of transcendental entire functions.
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