Geometric properties of caustics of pseudo-spherical surfaces

We deal with pseudo-spherical surfaces admitting certain singularities and their caustics. In particular, we give characterizations of cuspidal butterfly, cuspidal lip and cuspidal beak singularities on a pseudo-spherical surface. Moreover, characterizations of certain singularities on the caustics of a pseudo-spherical surface are given. Furthermore, when the caustic has a cuspidal edge singularity, we investigate geometric invariants defined at that point.