Non-invariant infinitely connected cycle of Baker domains

Abstract

We give the first example of a non-invariant cycle of Baker domains of infinite connectivity for non-entire meromorphic functions. We also prove the necessary and sufficient condition for a cycle of Baker domains to be infinitely connected in terms of critical points for the family \(f(z)=\lambda e^z+\frac{\mu }{z}\), where \(\lambda \) and \(\mu \) are defined in the paper.