CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS

摘要: This paper contains a survey of research on critical points smooth functions and their bifurcations. We indicate applications to the theory Lagrangian singularities (caustics), Legendre (wave fronts) asymptotic behaviour oscillatory integrals (the stationary phase method). describe connections with theories groups generated by reflections, automorphic forms, degenerations elliptic curves. give proofs theorems classification at most one modulus, also list all two moduli. The are based geometric technique associated Newton polygons, study roots certain Lie algebras resembling Enriques-Demazure fans, spectral sequences that constructed respect quasihomogeneous filtrations Koszul complex defined partial derivatives function.