Families of Baker domains for meromorphic functions with countable many essential singularities

Abstract

Given a transcendental meromorphic function that satisfies an asymptotic behaviour near infinity, Rippon and Stallard showed that such function has a family of invariant Baker domains associated to its essential singularity at infinity. In this work, we extend this result to meromorphic functions with a countable number of essential singularities. Furthermore, for any we provide a closed form description of a large class of functions with countable many essential singularities that exhibit p families of invariant Baker domains. This closed form allow us to provide explicit examples of the results.