Genericity of Caustics and Wavefronts on an r-corner

Abstract

We investigate genericities of reticular Lagrangian maps and reticular Legendrian maps in order to give generic classifications of caustics and wavefronts generated by a hypersurface germ without or with a boundary in a smooth manifold. We also give simpler proofs of main results in T. Tsukada, "Reticular Lagrangian Singularities," Asian J. Math., 1 (1997), pp. 572–622 and T. Tsukada, "Reticular Legendrian Singularities," Asian J. Math., 5:1 (2001), pp. 109–127.