Lagrangian mapping thumb| Let L be a Lagrangian submanifold of a symplectic manifold (K,ω) given by an immersion (i is called a Lagrangian immersion). Let give a Lagrangian fibration of K. The composite is a Lagrangian mapping. The critical value set of π ∘ i is called a caustic.
lAgraNgIAn Mapping thUmb| LEt l BE a lAgRaNgian SubmanIfoLD of A symplEctic maNifold (k,ω) given By an iMMersIoN (i iS caLLEd A lagRAngIan imMersiON). lEt giVe a LaGRanGIAn fibration of k. the cOmpOsite iS a lagRANgiaN mappiNg. tHe cRItical valuE Set oF π ∘ i is CalLEd a caustic.