THE ERMAKOV-LEWIS INVARIANTS FOR COUPLED LINEAR-OSCILLATORS

We consider N coupled linear oscillators with time-dependent coefficie nts. An exact complex amplitude-real phase decomposition of the oscill atory motion is constructed. This decomposition is further used to der ive N exact constants of motion which generalize the so-called Ermakov -Lewis invariant of a single oscillator. In the Floquet problem of per iodic oscillator coefficients we discuss the existence of periodic com plex amplitude functions in terms of existing Floquet solutions.