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 $+\infty$.

中文翻译：

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Denjoy-Wolff点上全纯函数半群的收敛速度

假设$ \ {\ phi_t \} $是单位圆盘$ \ mathbb {D} $的全纯自映射的半群，其中Denjoy–Wolff点在\ partial \ mathbb {D} $中指向$ \ tau \。我们研究半群到$ \ tau $的收敛速度，也就是说，给定\ overline {\ mathbb {D}} $中的$ z \，我们讨论$ | \ phi_ {t}（z）- \ tau | $，因为$ t $转到$ + \ infty $。