Abstract
We present a rigorous computation of the dynamical entropyh of the quantum Arnold cat map. This map, which describes a flow on the noncommutative two-dimensional torus, is a simple example of a quantum dynamical system with optimal mixing properties, characterized by Lyapunov exponents ± 1n λ+, λ+ > 1. We show that, for all values of the quantum deformation parameter,h coincides with the positive Lyapunov exponent of the dynamics.
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