Chaos for Liouville probability densities

Details Chaos for Liouville probability densities Chaos for Liouville probability densities

1995-06-05

arxiv.org/abs/chao-dyn/9506002v1

Nonlinear Sciences

Chaotic Dynamics

26 pages in REVTEX, no figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.53.3387

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the perturbation. The exponential rate of growth of the ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the map. These findings generalize and extend results obtained for the baker's map [R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].

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