Is dynamical chaos the same phenomenon in classical and quantum mechanical Hamiltonian systems?

A brief discussion of the Kolmogorov entropy interpretation of classical mechanical chaos and quantum mechanical chaos is given. It is pointed out that if a quantum mechanical Kolmogorov entropy is constructed to be analogous to a classical mechanical Kolmogorov entropy, then, for the case that the spectrum of the quantum mechanical system is discrete, the Kolmogorov entropy vanishes and there is no chaos, irrespective of the behavior of the corresponding classical mechanical system. A simple model which illustrates the deviation between classical and quantum dynamics with respect to chaos is also discussed.