On the convergence of boundary points for hyperbolic inner functions
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908680622964736 |
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| author | Jové, Anna Mencía, Mateo |
| author_facet | Jové, Anna Mencía, Mateo |
| contents | Given a hyperbolic inner function $f \colon \mathbb{D} \to \mathbb{D}$ with Denjoy-Wolff point $p \in \partial \mathbb{D}$, it is well known that almost every point $ξ\in \partial \mathbb{D}$ converges to $p$ under iteration of the radial extension $f^* \colon \partial \mathbb{D} \to \partial \mathbb{D}$. We provide explicit bounds for the rate of this convergence in terms of the angular derivative, holding almost surely. Our results also cover the case where the Denjoy-Wolff point is a singularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20502 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the convergence of boundary points for hyperbolic inner functions Jové, Anna Mencía, Mateo Dynamical Systems Given a hyperbolic inner function $f \colon \mathbb{D} \to \mathbb{D}$ with Denjoy-Wolff point $p \in \partial \mathbb{D}$, it is well known that almost every point $ξ\in \partial \mathbb{D}$ converges to $p$ under iteration of the radial extension $f^* \colon \partial \mathbb{D} \to \partial \mathbb{D}$. We provide explicit bounds for the rate of this convergence in terms of the angular derivative, holding almost surely. Our results also cover the case where the Denjoy-Wolff point is a singularity. |
| title | On the convergence of boundary points for hyperbolic inner functions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.20502 |