The global finite structure of generic envelope loci for Hamilton-Jacobi equations

We discuss in some detail the existence of global generating functions describing Lagrangian submanifolds connected with evolution problems for Hamilton–Jacobi H–J equations. First, we produce a physical application of a result by Viterbo: for generic in a suitable sense Hamiltonian functions and initial data, the envelopes, i.e., the wave front sets, related to Hamilton–Jacobi problems are globally finitely generated. Furthermore, we show how to compute global space–time generating functions with finite parameters for geometric solutions of a H–J equation of the evolution kind.