  Light rays passing very close to black holes may wind several times before
escaping. For any given electromagnetic source around the black hole, a distant
observer would thus observe two infinite sequences of images on either side of
the black hole. These images are generated by light rays performing an
increasing numbers of loops. The strong deflection limit provides a simple
analytic formalism to describe such higher order images for spherically
symmetric metrics, while for axially symmetric black holes one typically
resorts to numerical approaches. Here we present the leading order perturbation
to higher order images when the black hole spin is turned on. We show that the
images slide around the black hole shadow as an effect of space-time dragging.
We derive analytical formulae for their shifts and the perturbation of their
time delays. We also discuss how such simple analytical formulae for images by
Kerr black holes can be of great help in many applications.
