Baker domains with arbitrarily slow controlled rate of escape

Benjamin Handsaker-Whetton

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arXiv · 2609.37341

Baker domains with arbitrarily slow controlled rate of escape

Benjamin Handsaker-Whetton

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Abstract

Rempe and Rippon gave a general result which enables the construction of a transcendental entire function with a Baker domain, in which the iterates tend to infinity at a prescribed arbitrarily slow rate. Here we construct a transcendental entire function with a Baker domain, in which the iterates are controlled from both above and below in a prescribed arbitrarily slow but regular manner. The proof uses distortion theorems for conformal mappings due to Ahlfors and Warschawski, and an approximation theorem due to Rempe and Rippon.

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BibTeX RIS

Benjamin Handsaker-Whetton. 2026-09-29. Baker domains with arbitrarily slow controlled rate of escape. https://arxiv.org/abs/2609.37341

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