Singular orbits and Baker domains
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866916513451081728 |
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| author | Rempe, Lasse |
| author_facet | Rempe, Lasse |
| contents | We show that there is a transcendental meromorphic function with an invariant Baker domain $U$ such that every singular value of $f$ is a super-attracting periodic point. This answers a question of Bergweiler from 1993. We also show that $U$ can be chosen to contain arbitrarily large round annuli, centred at zero, of definite modulus. This answers a question of Mihaljević and the author from 2013, and complements recent work of Barański et al concerning this question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_07020 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Singular orbits and Baker domains Rempe, Lasse Dynamical Systems Complex Variables 37F10 (primary), 30D05, 37F31 (secondary) We show that there is a transcendental meromorphic function with an invariant Baker domain $U$ such that every singular value of $f$ is a super-attracting periodic point. This answers a question of Bergweiler from 1993. We also show that $U$ can be chosen to contain arbitrarily large round annuli, centred at zero, of definite modulus. This answers a question of Mihaljević and the author from 2013, and complements recent work of Barański et al concerning this question. |
| title | Singular orbits and Baker domains |
| topic | Dynamical Systems Complex Variables 37F10 (primary), 30D05, 37F31 (secondary) |
| url | https://arxiv.org/abs/2009.07020 |