Singular values and bounded Siegel disks

Let f be an entire transcendental function of finite order and Delta be a forward invariant bounded Siegel disk for f with rotation number in Herman's class (Formula presented.). We show that if f has two singular values with bounded orbit, then the boundary of Δ contains a critical point. We also give a criterion under which the critical point in question is recurrent. We actually prove a more general theorem with less restrictive hypotheses, from which these results follow.