R. Kargar

Characterizations of extremal hyperbolic rates via Herglotz measures and Koenigs linearization

Let $g:\mathbb{D}\to\mathbb{D}$ be a hyperbolic holomorphic self-map of the unit disk with Denjoy--Wolff point $\tau\in\partial\mathbb{D}$ and angular derivative $\alpha\in(0,1)$. We say that $g$ has an \textit{extremal hyperbolic rate} if its forward iterates satisfy the sharp metric asymptotic \begin{equation*} \rho_...