On slow escaping and non-escaping points of quasimeromorphic mappings
We show that for any quasimeromorphic mapping with an essential singularity at infinity, there exist points whose iterates tend to infinity arbitrarily slowly. This extends a result by Nicks for quasiregular mappings, and Rippon and Stallard for transcendental meromorphic functions on the complex pl...
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| Veröffentlicht in: | Ergodic theory and dynamical systems 2021-04, Vol.41 (4), p.1190-1216 |
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| container_title | Ergodic theory and dynamical systems |
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| creator | WARREN, LUKE |
| description | We show that for any quasimeromorphic mapping with an essential singularity at infinity, there exist points whose iterates tend to infinity arbitrarily slowly. This extends a result by Nicks for quasiregular mappings, and Rippon and Stallard for transcendental meromorphic functions on the complex plane. We further establish a new result for the growth rate of quasiregular mappings near an essential singularity, and briefly extend some results regarding the bounded orbit set and the bungee set to the quasimeromorphic setting. |
| doi_str_mv | 10.1017/etds.2019.110 |
| format | Article |
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| ispartof | Ergodic theory and dynamical systems, 2021-04, Vol.41 (4), p.1190-1216 |
| issn | 0143-3857 1469-4417 |
| language | eng |
| recordid | cdi_proquest_journals_2430606988 |
| source | Cambridge University Press Journals Complete |
| subjects | Infinity Mapping Meromorphic functions Original Article Singularity (mathematics) |
| title | On slow escaping and non-escaping points of quasimeromorphic mappings |
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