95-137 Slawomir Klimek, Andrzej Lesniewski

Quantized chaotic dynamics and non-commutative KS entropy (52K, plain TeX) Mar 7, 95

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 95-137.tex