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Quantization of the orientation preserving automorphisms of the torus. (English) Zbl 0777.58017

The quantization of any hyperbolic symplectomorphism of the two- dimensional torus is described by the finite dimensional irreducible representations of its naturally associated Weyl algebra. Furthermore the even part of the spectrum of the quantum propagator is characterized in terms of the orbits of the symplectomorphism.

MSC:

37D99 Dynamical systems with hyperbolic behavior
46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory
81S10 Geometry and quantization, symplectic methods
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References:

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