<p>This paper investigates the properties of trajectories in harmonic oscillator systems equipped with a point, absolutely continuous, or singular measure. Infinite-dimensional linear flows of countable oscillator systems exhibit a new class of trajectory behavior. Specifically, these trajectories are non-periodic, and their projections onto any four-dimensional symplectic subspace fail to be dense in the corresponding projection of the invariant torus. Such trajectories do not arise in finite-dimensional systems, are non-generic for countable oscillator systems, but become generic in the continual case. It is proved that for a countable harmonic oscillators system, every point on a nondegenerate invariant torus is a non-wandering point of the flow. Conversely, for a continuous system with an absolutely continuous measure, all points on such a torus are wandering. Furthermore, for continuous systems with singular measure, sufficient conditions on the measure and the torus are established, excluding the existence of both transitive trajectories and non-wandering points. As an application, a class of singular Bernoulli measures satisfying these conditions is presented.</p>