Deformation of Entire Functions with Baker Domains

We consider entire transcendental functions f with an invariant (or periodic) Baker Domain. First, we classify these domains into three types (hyperbolic, simply parabolic and doubly parabolic) according to the surface they induce when we take the quotient by the dynamics. Second, we study the space of quasiconformal deformations of an entire map with such a Baker Domain by studying its Teichmuller Space.