  We present a unified framework for the quantization of a family of discrete
dynamical systems of varying degrees of "chaoticity". The systems to be
quantized are piecewise affine maps on the two-torus, viewed as phase space,
and include the automorphisms, translations and skew translations. We then
treat some discontinuous transformations such as the Baker map and the
sawtooth-like maps. Our approach extends some ideas from geometric quantization
and it is both conceptually and calculationally simple.
