Inna Basak (Universitat Politècnica de Catalunya): Bifurcation analysis of Rubanovskii system via bi-Hamiltonian approach.

We discuss about some properties of bifurcation
diagram of the gyroscopic generalization of the Steclov-Lyapunov
integrable case of Kirchoff equation - Rubanovskii system,
describing the motion of a gyrostat in an ideal fluid.
Using the fact that Rubanovskii system is a bi-Hamiltonian
system and applying techniques for analysis of singularities
of bi-Hamiltonian system developed by A.Bolsinov, A.Oshemkov
we solve the following problems: description of the
singularities of the momentum mapping defined by four first
integrals of the system, stability analysis for closed
trajectories, non-degenaracy and stability
analysis for equilibria.