Classification of Singularities and Bifurcations of Critical Points of   Even Functions
  Singularities of even smooth functions are studied. A classification of singular points which appear in typical parametric families of even functions with at most five parameters is given. Bifurcations of singular points near a caustic value of the parameter are also studied. A determinant for singularity types and conditions for versal deformations are given in terms of partial derivatives (not requiring a preliminary reduction to a canonical form). 
E.A.Kudryavtseva, E.Lakshtanov
math.DG math-ph math.DS math.MP