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arXiv · 2503.20388

On the rates of convergence of orbits in semigroups of holomorphic functions

Dimitrios Betsakos·Francisco J. Cruz-Zamorano·Konstantinos Zarvalis
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Abstract

Let $(\phi_t)$ be a continuous semigroup of holomorphic self-maps of the unit disk $\mathbb{D}$ with Denjoy-Wolff point $\tau\in\overline{\mathbb{D}}$. We study the rate of convergence of the forward orbits of $(\phi_t)$ to the Denjoy-Wolff point by finding explicit bounds for the quantity $|\phi_t(z)-\tau|$, $z\in\overline{\mathbb{D}}$, $t > 0$. We further discuss the corresponding rate of convergence for the backward orbits of $(\phi_t)$.

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Dimitrios Betsakos, Francisco J. Cruz-Zamorano, Konstantinos Zarvalis. 2025-03-26. On the rates of convergence of orbits in semigroups of holomorphic functions. https://arxiv.org/abs/2503.20388

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