Compressor performance, absolutely! - Data Compression Conference, 2002. Proceedings. DCC 2002
نویسنده
چکیده
Kolmogorov (1958) recognised that by appropriately encoding phase-space trajectories of dynamical systems, one could in principle compute the corresponding Shannon entropies (in physics, referred to as the Kolmogorov-Sinai entropy) for each. Pesin [1] (1977) proved that for certain classes of dissipative non-linear systems, including one dimensional maps, the KS-entropy is precisely the sum of the positive Lyapunov exponents, effectively a measure of the global average tendency for initially close neighbour states to diverge exponentially with time. For the logistic map, certain coarse grained encodings of the phase space trajectories obtained from known generating partitions, yield finite alphabetic strings whose entropies are computable by way of the positive Lyapunov exponents.
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