  We show that an infinite set of q-deformed relevant operators close a partial
q-deformed Lie algebra under commutation with the Arik-Coon oscillator. The
dynamics is described by the multicommutator: [H,..., [H, O]...], that follows
a power law which leads to a dynamical scaling. We study the dynamics of the
Arik-Coon and anharmonic oscillators and analyze the role of q and the other
parameters in the evolution of both systems.
