For larger even , the Hamiltonians identify with the maximal number of independent invariants of motion (cf. Conserved quantity) characterizing a superintegrable system which evolves in -dimensional phase space. Such systems are also describable by conventional Hamiltonian dynamics; but their description in the framework of Nambu mechanics is substantially more elegant and intuitive, as all invariants enjoy the "same" geometrical status as the Hamiltonian: the trajectory in phase space is the intersection of the hypersurfaces specified by these invariants. Thus, the flow is perpendicular to all gradients of these Hamiltonians, whence parallel to the generalized cross product specified by the respective Nambu bracket.