Janeczko, Stanisław; Roberts, Mark Classification of symmetric caustics. I: Symplectic equivalence. (English) Zbl 0747.58015 Singularity theory and its applications. Pt. II: Singularities, bifurcations and dynamics, Proc. Symp., Warwick/UK 1988-89, Lect. Notes Math. 1463, 193-219 (1991). [For the entire collection see Zbl 0723.00029.]The authors generalize the classification theory of Arnol’d and Zakalyukin for singularities of Lagrange projections to projections that commute with a symplectic action of a compact Lie group up to symplectic equivalence. The theory is applied to the classification of infinitesimally stable corank 1 projections with \(Z_ 2\) symmetry.Their approach to symplectic equivalence is a generalization of the non- equivariant theory of Arnol’d and Zakalyukin in that they use a form of parametrized right equivalence of Morse functions. Reviewer: M.Adachi (Kyoto) Cited in 4 Documents MSC: 58C25 Differentiable maps on manifolds 58K99 Theory of singularities and catastrophe theory 58E09 Group-invariant bifurcation theory in infinite-dimensional spaces Keywords:singualrities of smooth maps; Lagrange submanifold; symplectic action Citations:Zbl 0723.00029 PDFBibTeX XMLCite \textit{S. Janeczko} and \textit{M. Roberts}, Lect. Notes Math. 1463, 193--219 (1991; Zbl 0747.58015)