Conformal conjugacies in Baker domains

Let F be a meromorphic function in the complex plane. We investigate the be haviour of the iterates of F in a Baker domain B. In particular, we describ e the dynamics of the orbits with the help of conformal conjugacies; that i s, we determine a function yl which is univalent in a large simply connecte d subdomain of B such that phi(F(z)) = T(phi(z)) holds throughout B. Here T is either a parabolic or hyperbolic Mobius transformation mapping either a half plane or C onto itself. This functional equation is always solvable i n a Baker domain if F has only finitely many poles. Moreover, there is an e xample of a function with infinitely many poles where one cannot find an ap propriate conformal conjugacy in an invariant Baker domain.