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As far as I know, the movement of a harmonic oscillator normally is not considered to be chaotic. Why not? Since the angular frequency can never be known to absolute precision, an error in the phase builds up. I can see that this build-up is only linear in time (if we assume the angular frequency to be constant), but since the phase only matters modulo 2π, φ(t) mod 2π is completely unpredictable time after some long enough time t. Isn't this exactly what chaos is about?