The angular derivative problem for petals of one-parameter semigroups in the unit disk
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913187352281088 |
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| author | Gumenyuk, Pavel Kourou, Maria Roth, Oliver |
| author_facet | Gumenyuk, Pavel Kourou, Maria Roth, Oliver |
| contents | We study the angular derivative problem for petals of one-parameter semigroups of holomorphic self-maps of the unit disk. For hyperbolic petals we prove a necessary and sufficient condition for the conformality of the petal in terms of the intrinsic hyperbolic geometry of the petal and the backward dynamics of the semigroup. For parabolic petals we characterize conformality of the petal in terms of the asymptotic behaviour of the Koenigs function at the Denjoy-Wolff point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_00700 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The angular derivative problem for petals of one-parameter semigroups in the unit disk Gumenyuk, Pavel Kourou, Maria Roth, Oliver Complex Variables Dynamical Systems Primary 37F44, 30D05, 30D40, 30C35, Secondary 37C10, 37C25, 30C80 We study the angular derivative problem for petals of one-parameter semigroups of holomorphic self-maps of the unit disk. For hyperbolic petals we prove a necessary and sufficient condition for the conformality of the petal in terms of the intrinsic hyperbolic geometry of the petal and the backward dynamics of the semigroup. For parabolic petals we characterize conformality of the petal in terms of the asymptotic behaviour of the Koenigs function at the Denjoy-Wolff point. |
| title | The angular derivative problem for petals of one-parameter semigroups in the unit disk |
| topic | Complex Variables Dynamical Systems Primary 37F44, 30D05, 30D40, 30C35, Secondary 37C10, 37C25, 30C80 |
| url | https://arxiv.org/abs/2303.00700 |