THE DYNAMICAL ENTROPY OF THE QUANTUM ARNOLD CAT MAP

We present a rigorous computation of the dynamical entropy h of the qu antum Arnold cat map. This map, which describes a flow on the noncommu tative two-dimensional torus, is a simple example of a quantum dynamic al system with optimal mixing properties, characterized by Lyapunov ex ponents +/-In lambda(+), lambda(+) > 1. We show that, for all values o f the quantum deformation parameter, h coincides with the positive Lya punov exponent of the dynamics.