Topology of bifurcation diagrams of integrable systems on semisimple Lie algebras. (Q1432410)

There exists a large class of integrable systems on the orbits of coadjoint representations of Lie algebras. Studying the topology of bifurcation diagrams for the systems under consideration requires finding points where the rank of the moment map drops. The presented results make it possible to find various critical points and to describe their properties in terms of the algebraic structure without evaluation of the rank of the Jacobian. In particular, for shifts of invariants of compact semisimple algebras, a complete description of points is obtained at which the rank of the differential of the moment map equals to 0 or 1.