Bifurcations of Baker domains

Abstract

We consider the family of transcendental entire functions given by . If Re c > 0, then fc features a Baker domain as the only component of the Fatou set, while the functions fc show a different dynamical behaviour if . We describe the dynamical planes of these functions and show that the Julia sets converge in the limit process with respect to the Hausdorff metric, where and . We use this to show that Baker domains of any type (concerning a classification of König) are not necessarily stable under perturbation.