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

Let $({\phi }_t)$ be a continuous semigroup of holomorphic self-maps of the unit disk $\mathbb{D}$ with Denjoy-Wolff point $\tau \in \bar{\mathbb{D}}$. 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 $\mathrm{\mid }{\phi }_t(z)-\tau \mathrm{\mid }$, $z\in \bar{\mathbb{D}}$, $t>0$. We further discuss the corresponding rate of convergence for the backward orbits of $({\phi }_t)$.