Some examples of Baker domains

TL;DR

This paper constructs entire functions with specific Baker domains that are not univalent, providing new examples and extending Riemann maps continuously, thus answering several open questions in complex dynamics.

Contribution

It introduces novel entire functions with hyperbolic and parabolic Baker domains where the functions are not univalent, advancing understanding of Baker domain structures.

Findings

Constructed entire functions with non-univalent Baker domains

Extended Riemann maps continuously to certain arcs

Addressed open questions in complex dynamics

Abstract

We construct entire functions with hyperbolic and simply parabolic Baker domains on which the functions are not univalent. The Riemann maps from the unit disk to these Baker domains extend continuously to certain arcs on the unit circle. The results answer questions posed by Fagella and Henriksen, Baker and Dominguez, and others.