In this paper, we discover new connections between topics in classical geometric function theory and complex dynamics. In particular, we study some classes of starlike functions and their embeddings in the classes of semigroup generators. In addition, we find explicit formulas for the radii of starlikeness for those classes and uniform rates of convergence of semigroups to their Denjoy–Wolff points.

中文翻译：

---

星形函数和半群生成器的半径问题

在本文中，我们发现了经典几何函数理论与复杂动力学之间的新联系。特别是，我们研究了一些类星函数及其在半群生成器类中的嵌入。此外，我们找到了这些类别的星形半径和半群到其Denjoy-Wolff点的一致收敛速率的明确公式。