Periodic boundary points for simply connected Fatou components of transcendental maps
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929316879663104 |
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| author | Jové, Anna |
| author_facet | Jové, Anna |
| contents | Let f be a transcendental map, and let U be an attracting or parabolic basin, or a doubly parabolic Baker domain. Assume U is simply connected. Then, we prove that periodic points are dense in the boundary of U, under certain hypothesis on the postsingular set. This generalizes a result by F. Przytycki and A. Zdunik for rational maps. Our proof uses techniques from measure theory, ergodic theory, conformal analysis, and inner functions. In particular, a result on the distortion of inner functions near the unit circle is provided, which is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Periodic boundary points for simply connected Fatou components of transcendental maps Jové, Anna Dynamical Systems Let f be a transcendental map, and let U be an attracting or parabolic basin, or a doubly parabolic Baker domain. Assume U is simply connected. Then, we prove that periodic points are dense in the boundary of U, under certain hypothesis on the postsingular set. This generalizes a result by F. Przytycki and A. Zdunik for rational maps. Our proof uses techniques from measure theory, ergodic theory, conformal analysis, and inner functions. In particular, a result on the distortion of inner functions near the unit circle is provided, which is of independent interest. |
| title | Periodic boundary points for simply connected Fatou components of transcendental maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2404.11094 |