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Baker domains with arbitrarily slow controlled rate of escape
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
@misc{handsakerwhetton2026baker,
title = {{Baker domains with arbitrarily slow controlled rate of escape}},
author = {Benjamin Handsaker-Whetton},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37341},
eprint = {2609.37341},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37341},
}
RIS
TY - UNPB
TI - Baker domains with arbitrarily slow controlled rate of escape
AU - Benjamin Handsaker-Whetton
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37341
UR - https://arxiv.org/abs/2609.37341
AB - 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.
ER -