Some examples of Baker domains

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.

13 pages

References in corpus (2)

• Iteration of meromorphic functions
• Baker domains for Newton's method

Cited by in corpus (5)

• Absorbing sets and Baker domains for holomorphic maps
• Escaping points in the boundaries of Baker domains
• The escaping set in transcendental dynamics
• Escaping Fatou components of transcendental self-maps of the punctured plane
• Interactions between Universal Composition Operators and Complex Dynamics