Simply connected Baker domains of some meromorphic functions

The first example of a meromorphic function with non-invariant Baker domains was published by Baker et al. (1991) [2]. In this article we answer some questions concerning connectivity of Baker domains of that meromorphic function and location of the iterates of critical values. We analyze dynamics on the Fatou set and connectivity of the Julia set. We extend some of the achieved results to the family fλ,μ(z)=λexp(z)+μz of transcendental meromorphic functions, where λ,μ∈C∖{0}. We also prove that some 'non-parabolic' bifurcations appear many times in this family.