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This is intended as an introduction to and review of the work of V, Arnoldand his collaborators on the theory of Lagrangian and Legendrian submanifoldsand their associated maps. The theory is illustrated by applications toHamilton-Jacobi theory and the eikonal equation, with an emphasis on nullsurfaces and wavefronts and their associated caustics and singularities.Comment: Figs. not include

The theory of caustics and wave front singularities with physical applications