Critical subsystems of the Kowalevski gyrostat in two constant fields

The Kowalevski gyrostat in two constant fields is known as the unique profound example of an integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems in fewer dimensions. As the first approach to topological analysis of this system we find the critical set of the integral map; this set consists of the trajectories with number of frequencies less than three. We obtain the equations of the bifurcation diagram in three-dimensional space of the first integrals constants.