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Keywords
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Keywords: integrable Hamiltonian systems, isoenergy surfaces, Kirchhoff equations, Liouville
foliation, bifurcation diagram, Borisov –Mamaev – Sokolov case, topological invariant
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Abstract
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Abstract—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 Poincar´e equations on the Lie
algebra so(4), which describe the motion of a body with cavities filled with an incompressible
vortex fluid. Moreover, the Poincar´e 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.
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