95-33 S. De Bievre, M. Degli Esposti, R. Giachetti
Quantization of a class of piecewise affine transformations on the torus (70K, AMS-TeX) Jan 30, 95
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Abstract. 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.

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