Slawomir Klimek, Andrzej Lesniewski Quantized chaotic dynamics and non-commutative KS entropy (52K, plain TeX) ABSTRACT. We study the quantization of a classically chaotic dynamics, the Anosov dynamics of ``cat maps'' on a two dimensional torus. This dynamics is implemented as a discrete group of automorphisms of a von Neumann algebra of functions on a quantized torus. We compute the non-commutative generalization of the Kolmogorov-Sinai entropy, namely the Connes-St\o rmer entropy, of the generator of this group, and find that its value is equal to the classical value. This can be interpreted as a sign of stability of chaotic behavior in a dynamical system under quantization.