I working on a problem involving periodic vs. non-periodic 2-d anisotropic linear oscillators. I am trying to understand why it is that for a ratio of angular velocities that is rational, the motion of the oscillator is periodic. Versus the case where the ratio of angular velocities in irrational. From what I can understand thus far it really comes down to whether or not a least common multiple exists. For the case where the angular velocity ratio is rational, a least common multiple clearly exists. There is some definite time interval at which the motion will repeat itself. For the case where the ratio is irrational, there is no exact least common multiple for periods of motion. Is this correct? Am I missing something? Comments appreciated.