Maria Kourou (University of Würzburg)
will speak on
Models and pre-models for holomorphic self-maps of the unit disk
Time: 3:00PM
Date: Tue 17th February 2026
Location: E0.32 (beside Pi restaurant)
[map]
Further informationAbstract: Let $\varphi$ be a holomorphic self-map of the unit disk $\mathbb{D}$, having no interior fixed points. In the talk, we explore various aspects of both forward and backward dynamics of $\varphi$. Under appropriate normalizations, there exists a unique triple $(\Omega_0, \sigma,z\mapsto z+1)$, where $\Omega_0$ is a domain in $\mathbb{C}$ and $\sigma:\mathbb{D} \to \Omega_0$ is a holomorphic function, which is said to be a model for $\varphi$.
The function $\sigma$ is called the Koenigs function of $\varphi$. We discuss latest advances on the boundary behavior of the Koenigs function $\sigma$ for all possible cases of the holomorphic map $\varphi$. Concentrating on the backward dynamics of $\varphi$, suppose that $\xi \in \partial \mathbb{D}$ is a repulsive fixed point of $\varphi$. Then the function $\varphi$ admits a triple $(\mathbb{D}, g, \eta)$ at $\xi$, where $\eta$ is a conformal automorphism of $\mathbb{D}$ and $g$ is a holomorphic self-map of $\mathbb{D}$, which is called a pre-model for $\varphi$ at $\xi$. In this context, we study necessary and sufficient conditions so that the pre-model at $\xi$ is regular.
The results presented are based on joint works with M. Contreras, F. Cruz-Zamorano, L. Rodr{\'i}guez-Piazza, and P. Gumenyuk, A. Moucha, O. Roth.
https://ucd-ie.zoom.us/j/63071806994
(This talk is part of the Analysis series.)
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