  We generalize the definition of quantum Anosov properties and the related
Lyapunov exponents to the case of quantum systems driven by a classical flow,
i.e. skew-product systems. We show that the skew Anosov properties can be
interpreted as regular Anosov properties in an enlarged Hilbert space, in the
framework of a generalized Floquet theory. This extension allows us to describe
the hyperbolicity properties of almost-periodic quantum parametric oscillators
and we show that their upper Lyapunov exponents are positive and equal to the
Lyapunov exponent of the corresponding classical parametric oscillators. As
second example, we show that the configurational quantum cat system satisfies
quantum Anosov properties.
