A caustic may be seen on a wall, illuminated by rays of light reflected from a concave surface, for example the surface of a cup. By moving the cup one can see that generic caustics have only standard singularities, while more complicated singularities decompose into standard ones under small perturbations. In this Chapter we construct a tool for studying the singularities of caustics — the theory of Lagrangian singularities.
KeywordsPoisson Bracket Symplectic Manifold Symplectic Structure Cotangent Bundle Lagrangian Submanifold
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