CLASSIFICATION OF SYMMETRICAL CAUSTICS .1. SYMPLECTIC EQUIVALENCE

We generalise the classification theory of Arnold and Zakalyukin for singularities of Lagrange projections to projections that commute with a symplectic action of a compact Lie group. The theory is applied to the classification of infinitesimally stable corank 1 projections with Z2 symmetry. However examples show that even in very low dimensions there exist generic projections which are not infinitesimally stable.