Mathematics

Wave fronts of a hyperbolic system of two linear partial differential equations in three- dimensional space are described by the Fermat principle of least time if the admissible velocities at any point form an ellipse.   We describe some typical singularities of such fronts. It turns out there are two absolutely different cases: elliptic and hyperbolic. In particular, the sub-Riemannian sphere appear in the elliptic case and I am going to describe what happens in the hyperbolic case.