Baker domains with arbitrarily slow controlled rate of escape
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.
math.DS↗