  Let f be an entire function whose set of singular values is bounded and
suppose that f has a Siegel disk such that f restricts to a homeomorphism of
the boundary. We show that the Siegel disk is bounded. Using a result of
Herman, we deduce that if additionally the rotation number of the Siegel disk
is Diophantine, then its boundary contains a critical point of f.
  Suppose furthermore that all singular values of f lie in the Julia set. We
prove that, if f has a Siegel disk $U$ whose boundary contains no singular
values, then the condition that f is a homeomorphism of the boundary of U is
automatically satisfied. We also investigate landing properties of periodic
dynamic rays by similar methods.
