Compatibility of symplectic structures adapted to noncommutatively integrable systems (Q1299172)

The authors apply an approach based on the geometry of noncommutatively integrable systems to characterize from the point of symplectic geometry the family of several structures. Recent work by Bogoyavlenskij on nondegenerate Hamiltonian systems has been extended to degenerate systems which prove to be comparatively richer in symplectic structures. It is shown that the system is integrable if it is Hamiltonian with respect to the symplectic structures under study. Certain questions related to recursion operators and symmetries are considered.