In classical mechanics discrete area preserving maps give information on chaotic motion. The corresponding map in quantum systems is a unitary transformation giving the evolution of the state in a discrete time step. Balazs, and his collaborator, Voros, have discussed two such maps, the map for motion on a pseudosphere, a relatively nonphysical system, and the quantized Baker's map. It is proposed to complete this work, in particular to look at the large time behavior, and the passage to the classical limit, to test the correspondence between chaotic motion in the classical and quantum system.
