Smearing of chaos in sandwich pp-waves

Recent results demonstrating the chaotic behaviour of geodesics in non-homo geneous vacuum pp-wave solutions are generalized. Here we concentrate on mo tion in non-homogeneous sandwich pp-waves and show that chaos smears as the duration of these gravitational waves is reduced. As the number of radial bounces of any geodesic decreases, thr outcome channels to infinity become fuzzy, and thus the fractal structure of the initial conditions :characteri zing chaos is cut at lower and lower levels. In the limit of impulsive wave s, the motion is fully non-chaotic. This is proved by presenting the geodes ics in a simple explicit form which permits a physical interpretation, and demonstrates the focusing effect. It is shown that a circle of test particl es is deformed by the impulse into a family of closed hypotrochoidal curves in the transverse plane. These are deformed in the longitudinal direction in such a way that a specific closed caustic surface is formed.