  It is shown that, while Wigner and Liouville functions transform in an
identical way under linear symplectic maps, in general they do not transform
identically for nonlinear symplectic maps. Instead there are ``quantum
corrections'' whose hbar tending to zero limit may be very complicated.
Examples of the behavior of Wigner functions in this limit are given in order
to examine to what extent the corresponding Liouville densities are recovered.
