On the rates of convergence of orbits in semigroups of holomorphic functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916662862675968 |
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| author | Betsakos, Dimitrios Cruz-Zamorano, Francisco J. Zarvalis, Konstantinos |
| author_facet | Betsakos, Dimitrios Cruz-Zamorano, Francisco J. Zarvalis, Konstantinos |
| contents | Let $(ϕ_t)$ be a continuous semigroup of holomorphic self-maps of the unit disk $\mathbb{D}$ with Denjoy-Wolff point $τ\in\overline{\mathbb{D}}$. We study the rate of convergence of the forward orbits of $(ϕ_t)$ to the Denjoy-Wolff point by finding explicit bounds for the quantity $|ϕ_t(z)-τ|$, $z\in\overline{\mathbb{D}}$, $t > 0$. We further discuss the corresponding rate of convergence for the backward orbits of $(ϕ_t)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_20388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the rates of convergence of orbits in semigroups of holomorphic functions Betsakos, Dimitrios Cruz-Zamorano, Francisco J. Zarvalis, Konstantinos Complex Variables Primary: 30D05, 37F44, Secondary: 30C85, 31A15 Let $(ϕ_t)$ be a continuous semigroup of holomorphic self-maps of the unit disk $\mathbb{D}$ with Denjoy-Wolff point $τ\in\overline{\mathbb{D}}$. We study the rate of convergence of the forward orbits of $(ϕ_t)$ to the Denjoy-Wolff point by finding explicit bounds for the quantity $|ϕ_t(z)-τ|$, $z\in\overline{\mathbb{D}}$, $t > 0$. We further discuss the corresponding rate of convergence for the backward orbits of $(ϕ_t)$. |
| title | On the rates of convergence of orbits in semigroups of holomorphic functions |
| topic | Complex Variables Primary: 30D05, 37F44, Secondary: 30C85, 31A15 |
| url | https://arxiv.org/abs/2503.20388 |