# On the rate of convergence of semigroups of holomorphic functions at the Denjoy–Wolff point

### Dimitrios Betsakos

Aristotle University of Thessaloniki, Greece### Manuel D. Contreras

Universidad de Sevilla, Spain### Santiago Díaz-Madrigal

Universidad de Sevilla, Spain

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## Abstract

Let $\{\phi_t\}$ be a semigroup of holomorphic self-maps of the unit disc $\mathbb{D}$ with Denjoy–Wolff point $\tau\in \partial\mathbb{D}$. We study the rate of convergence of the semigroup to $\tau$, that is, given $z\in \overline{\mathbb{D}}$, we discuss the behavior of $|\phi_{t}(z)-\tau|$ as $t$ goes to $+\infty$.

## Cite this article

Dimitrios Betsakos, Manuel D. Contreras, Santiago Díaz-Madrigal, On the rate of convergence of semigroups of holomorphic functions at the Denjoy–Wolff point. Rev. Mat. Iberoam. 36 (2020), no. 6, pp. 1659–1686

DOI 10.4171/RMI/1179