Figure 2

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 (A ) 1, there are five kinds of stable points, known as fold (A2), cusp (A3), swallow-tail (A4), pyramid - (D 4 ), and purse + (D 4 ). The Ak and Dk notation refers to a relation to exceptional groups (see [11]). The picture is taken from [150].