  We study various corrections of correlation functions to leading order in
conformal perturbation theory, both on the cylinder and on the plane. Many
problems on the cylinder are mathematically equivalent to those in the plane if
we give the perturbations a position dependent scaling profile. The integrals
to be done are then similar to the study of correlation functions with one
additional insertion at the center of the profile. We will be primarily
interested in the divergence structure of these corrections when computed in
dimensional regularization. In particular, we show that the logarithmic
divergences (enhancements) that show up in the plane under these circumstances
can be understood in terms of resonant behavior in time dependent perturbation
theory, for a transition between states that is induced by an oscillatory
perturbation on the cylinder.
