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.