Grand orbit relations in wandering domains
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929357557071872 |
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| author | Evdoridou, Vasiliki Fagella, Núria Geyer, Lukas Pardo-Simón, Leticia |
| author_facet | Evdoridou, Vasiliki Fagella, Núria Geyer, Lukas Pardo-Simón, Leticia |
| contents | One of the fundamental distinctions in McMullen and Sullivan's description of the Teichmüller space of a complex dynamical system is between discrete and indiscrete grand orbit relations. We investigate these on the Fatou set of transcendental entire maps and provide criteria to distinguish between the two types. Furthermore, we show that discrete and indiscrete grand orbit relations may coexist non-trivially in a wandering domain, a phenomenon which does not occur for any other type of Fatou component. One of the tools used is a novel quasiconformal surgery technique of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15667 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Grand orbit relations in wandering domains Evdoridou, Vasiliki Fagella, Núria Geyer, Lukas Pardo-Simón, Leticia Dynamical Systems Complex Variables One of the fundamental distinctions in McMullen and Sullivan's description of the Teichmüller space of a complex dynamical system is between discrete and indiscrete grand orbit relations. We investigate these on the Fatou set of transcendental entire maps and provide criteria to distinguish between the two types. Furthermore, we show that discrete and indiscrete grand orbit relations may coexist non-trivially in a wandering domain, a phenomenon which does not occur for any other type of Fatou component. One of the tools used is a novel quasiconformal surgery technique of independent interest. |
| title | Grand orbit relations in wandering domains |
| topic | Dynamical Systems Complex Variables |
| url | https://arxiv.org/abs/2405.15667 |