GENERALIZED HAMILTONIAN STRUCTURES FOR SYSTEMS IN 3 DIMENSIONS WITH ARESCALABLE CONSTANT OF MOTION

The generalized Hamiltonian structures of several three-dimensional dy namical systems of interest in physical applications are considered. I n general, Hamiltonians exist only for systems that possess at least o ne time-independent constant of motion. Systems with only time-depende nt constants of motion may sometimes be rescaled and their constant of motion made time-independent. When this is possible, the transformed system may be cast in a generalized Hamiltonian formalism with non-can onical structure functions.