Ghorbanali Haghighatdoost

35 Km Tabriz-Maragheh Road, Tabriz, Iran
Azarbaijan Shahid Madani University


Akbarzadeh R., Haghighatdoost G.
In 2001, A.V. Borisov, I.S. Mamaev, and V.V. Sokolov discovered a new integrable case on the Lie algebra $so(4)$. This system coincides with the Poincaré equations on the Lie algebra $so(4)$, which describe the motion of a body with cavities filled with an incompressible vortex fluid. Moreover, the Poincaré equations describe the motion of a four-dimensional gyroscope. In this paper topological properties of this system are studied. In particular, for the system under consideration the bifurcation diagrams of the momentum mapping are constructed and all Fomenko invariants are calculated. Thereby, a classification of isoenergy surfaces for this system up to the rough Liouville equivalence is obtained.
Keywords: integrable Hamiltonian systems, isoenergy surfaces, Kirchhoff equations, Liouville foliation, bifurcation diagram, Borisov–Mamaev–Sokolov case, topological invariant
Citation: Akbarzadeh R., Haghighatdoost G.,  The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$, Regular and Chaotic Dynamics, 2015, vol. 20, no. 3, pp. 317-344

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