Bounded Fatou and Julia components of meromorphic functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917861668159488 |
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| author | Martí-Pete, David Rempe, Lasse Waterman, James |
| author_facet | Martí-Pete, David Rempe, Lasse Waterman, James |
| contents | We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions. On the one hand, we prove that a bounded domain is a Fatou component of some meromorphic function if and only if it is regular. On the other hand, we prove that a planar continuum is a Julia component of some meromorphic function if and only if it has empty interior. We do so by constructing meromorphic functions with wandering continua using approximation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_11781 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bounded Fatou and Julia components of meromorphic functions Martí-Pete, David Rempe, Lasse Waterman, James Dynamical Systems Complex Variables 37F10 (primary), 30D05, 37B45, 54F15 (secondary) We completely characterise the bounded sets that arise as components of the Fatou and Julia sets of meromorphic functions. On the one hand, we prove that a bounded domain is a Fatou component of some meromorphic function if and only if it is regular. On the other hand, we prove that a planar continuum is a Julia component of some meromorphic function if and only if it has empty interior. We do so by constructing meromorphic functions with wandering continua using approximation theory. |
| title | Bounded Fatou and Julia components of meromorphic functions |
| topic | Dynamical Systems Complex Variables 37F10 (primary), 30D05, 37B45, 54F15 (secondary) |
| url | https://arxiv.org/abs/2204.11781 |