  The use of the quantizer-dequantizer formalism to describe the evolution of a
quantum system is reconsidered. We show that it is possible to embed a manifold
in the space of quantum states of a given auxiliary system by means of an
appropriate quantizer-dequantizer system. If this manifold of states is
invariant with respect to some unitary evolution, the quantizer-dequantizer
system provides a classical-like realization of such dynamics, which in general
is non linear. Integrability properties are also discussed. Weyl systems and
generalized coherente states are used as a simple illustration of these ideas.
