  We consider a quantum many-body system - the Bose-Hubbard system on three
sites - which has a classical limit, and which is neither strongly chaotic nor
integrable but rather shows a mixture of the two types of behavior. We compare
quantum measures of chaos (eigenvalue statistics and eigenvector structure) in
the quantum system, with classical measures of chaos (Lyapunov exponents) in
the corresponding classical system. As a function of energy and interaction
strength, we demonstrate a strong overall correspondence between the two cases.
In contrast to both strongly chaotic and integrable systems, the largest
Lyapunov exponent is shown to be a multi-valued function of energy.
