Lagrange singularities under symplectic reduction (Q1264738)

The authors give a classification of simple Lagrangian germs arising via arbitrary symplectic reduction up to the wider equivalence group of all symplectomorphisms. A similar problem on singularities of symplectic reduction (however, with respect to fibration-preserving symplectomorphisms) was also considered by \textit{W. Domitrz} and \textit{S. Janeczko} in [Banach Cent. Publ. 39, 31-37 (1997; Zbl 0881.57028)]. The first singularity class of Morse nontransversality is considered in more detail. It is proved to be stable using equivalences from a smaller group which consist of symplectomorphisms preserving a foliation of the ambient symplectic space, one of the leaves being the given co-isotropic hypersurface. This singularity class is used to estimate the number of trajectories of a natural mechanical system issuing from a given submanifold of the configuration space and reaching the boundary of the region of admissible motion.