95-137 Slawomir Klimek, Andrzej Lesniewski
Quantized chaotic dynamics and non-commutative KS entropy (52K, plain TeX) Mar 7, 95
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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.

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