THE LIOUVILLE CONDITION AND NAMBU MECHANICS

It is shown that if a system of coupled differential equations satisfi es the Louville condition it is not necessarily constructed according to the Nambu prescripton. The relation of the number of time-independe nt integrals of the system to the required number of Hamiltonians is e xplored. The extended version of Nambu mechanics that admits singlets is related to the generalized Hamiltonian version of dynamics. All fea tures are explored within one specific example in three-dimensional ph ase space.