THE QUANTIZED D-TRANSFORMATION

We construct a new example of a quantum map, the quantized version of the D-transformation, which is the natural extension to two dimensions of the tent map. The classical, quantum and semiclassical behavior is studied. We also exhibit some relationships between the quantum versi ons of the D-map and the parity projected baker's map. The method of c onstruction allows a generalization to dissipative maps which includes the quantization of a horseshoe. (C) 1996 American Institute of Physi cs.