A semiclassical formula is derived for the Wigner representation of the quasi-energy states of a quantum map on a torus. It is expressed as a finite sum over the classical fixed points of the map. A criterion for the appearance of 'scars' is presented. Semiclassical Wigner functions of the cat map are calculated and shown to reproduce the exact quantum mechanical results.
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Agam et al. (1995) studied this question.
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