The size and topology of quasi-Fatou components of quasiregular maps
We consider the iteration of quasiregular maps of transcendental type from Rd to Rd. In particular we study quasi-Fatou 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 f...
| Main Authors: | , |
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| Format: | Article |
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American Mathematical Society
2017
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| Online Access: | https://eprints.nottingham.ac.uk/35153/ |
| _version_ | 1848795014969163776 |
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| author | Nicks, Daniel A. Sixsmith, David J. |
| author_facet | Nicks, Daniel A. Sixsmith, David J. |
| author_sort | Nicks, Daniel A. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We consider the iteration of quasiregular maps of transcendental type from Rd to Rd. In particular we study quasi-Fatou 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 quasi-Fatou components. First, we study the number of com- plementary components of quasi-Fatou components, generalising, and slightly strengthening, a result of Kisaka and Shishikura. Second, we study the size of quasi-Fatou 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. |
| first_indexed | 2025-11-14T19:25:22Z |
| format | Article |
| id | nottingham-35153 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:25:22Z |
| publishDate | 2017 |
| publisher | American Mathematical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-351532020-05-04T18:23:10Z https://eprints.nottingham.ac.uk/35153/ The size and topology of quasi-Fatou components of quasiregular maps Nicks, Daniel A. Sixsmith, David J. We consider the iteration of quasiregular maps of transcendental type from Rd to Rd. In particular we study quasi-Fatou 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 quasi-Fatou components. First, we study the number of com- plementary components of quasi-Fatou components, generalising, and slightly strengthening, a result of Kisaka and Shishikura. Second, we study the size of quasi-Fatou 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. American Mathematical Society 2017-01-01 Article PeerReviewed Nicks, Daniel A. and Sixsmith, David J. (2017) The size and topology of quasi-Fatou components of quasiregular maps. Proceedings of the American Mathematical Society, 145 (2). pp. 749-763. ISSN 1088-6826 http://www.ams.org/journals/proc/2017-145-02/S0002-9939-2016-13253-X/ doi:10.1090/proc/13253 doi:10.1090/proc/13253 |
| spellingShingle | Nicks, Daniel A. Sixsmith, David J. The size and topology of quasi-Fatou components of quasiregular maps |
| title | The size and topology of quasi-Fatou components of quasiregular maps |
| title_full | The size and topology of quasi-Fatou components of quasiregular maps |
| title_fullStr | The size and topology of quasi-Fatou components of quasiregular maps |
| title_full_unstemmed | The size and topology of quasi-Fatou components of quasiregular maps |
| title_short | The size and topology of quasi-Fatou components of quasiregular maps |
| title_sort | size and topology of quasi-fatou components of quasiregular maps |
| url | https://eprints.nottingham.ac.uk/35153/ https://eprints.nottingham.ac.uk/35153/ https://eprints.nottingham.ac.uk/35153/ |