Figure 2: Wave fronts that are locally stable in the sense of Arnold. Each picture shows the projection into 3-space of a wave-front, locally near a caustic point. The projection is made along the integral curves of a timelike vector field. The qualitative features are independent of which timelike vector field is chosen. In addition to regular, i.e., non-caustic, points , there are five kinds of stable points, known as fold , cusp , swallow-tail , pyramid , and purse . The and notation refers to a relation to exceptional groups (see [11]). The picture is taken from [149].