  The Kowalevski gyrostat in two constant fields is known as the unique example
of an integrable Hamiltonian system with three degrees of freedom not reducible
to a family of systems in fewer dimensions and still having the clear
mechanical interpretation. The practical explicit integration of this system
can hardly be obtained by the existing techniques. Then the challenging problem
becomes to fulfil the qualitative investigation based on the study of the
Liouville foliation of the phase space. As the first approach to topological
analysis of this system we find the stratified critical set of the momentum
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. These equations have the form convenient for the classification of the
bifurcation sets induced on 5-dimensional iso-energetic levels.
