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

Dynamical aspects in the Quantizer-Dequantizer formalism