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

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 $+\infty$.