QUANTIZATION OF ANOSOV MAPS

Cat maps, linear automorphisms of the torus, are standard examples of classically chaotic systems, but they are periodic when quantized, lea ding to many untypical consequences. Anosov maps are topologically equ ivalent to cat maps despite being nonlinear. Generalizing the original quantization of cat maps, we establish that quantum Anosov maps have typical spectral fluctuations for classically chaotic systems. The per iodic orbit theory for the spectra of quantum Anosov maps is not exact , as it is for cat maps. Nonetheless our calculations verify that the semiclassical trace of the propagator is accurate well beyond any ''lo g time'' cutoff. (C) 1995 Academic Press. Inc.