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MORSES LEMMA AND SOME GENERALIZATIONS
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action acts apply associated assume asymptotic bundle called Chapter choice choose clear closed compact complex computation condition connected consider consists constant coordinates corresponding curve defined definition denote depend describe determines diffeomorphism differential dimensional discuss element equation example exists expression fact fiber fixed follows formula function given gives graph half density half form hence homogeneous identify induced integral invariant Lagrangian Lagrangian submanifold Lagrangian subspace lemma Lie algebra linear manifold matrix metalinear multiplication neighborhood Notice obtain operator orbits pairing parametrization particular phase polarization positive projection proof Proposition prove representation satisfies singularities smooth solution space structure Suppose symbol tangent tangent vector theorem transform transversal values vanishes vector bundle vector field vector space wave write zero