We consider the case of an exponential map for which the singular value is
accessible from the set of escaping points. We show that there are dynamic rays
of which do not land. In particular, there is no analog of Douady's ``pinched
disk model'' for exponential maps whose singular value belongs to the Julia
set.
We also prove that the boundary of a Siegel disk U for which the singular
value is accessible both from the set of escaping points and from U contains
uncountably many indecomposable continua.Comment: 15 pages; 1 figure. V2: A result on Siegel disks, as well as a
figure, has been added. Some minor corrections were also mad
