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A General Symbolic Approach to Kolmogorov-Sinai Entropy

Institute of Mathematics, University of Lübeck, Ratzeburger Allee 160, 23562 Lübeck, Germany
Author to whom correspondence should be addressed.
Entropy 2017, 19(12), 675;
Received: 31 October 2017 / Revised: 4 December 2017 / Accepted: 5 December 2017 / Published: 9 December 2017
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
PDF [390 KB, uploaded 19 December 2017]


It is popular to study a time-dependent nonlinear system by encoding outcomes of measurements into sequences of symbols following certain symbolization schemes. Mostly, symbolizations by threshold crossings or variants of it are applied, but also, the relatively new symbolic approach, which goes back to innovative works of Bandt and Pompe—ordinal symbolic dynamics—plays an increasing role. In this paper, we discuss both approaches novelly in one breath with respect to the theoretical determination of the Kolmogorov-Sinai entropy (KS entropy). For this purpose, we propose and investigate a unifying approach to formalize symbolizations. By doing so, we can emphasize the main advantage of the ordinal approach if no symbolization scheme can be found that characterizes KS entropy directly: the ordinal approach, as well as generalizations of it provide, under very natural conditions, a direct route to KS entropy by default. View Full-Text
Keywords: symbolization; KS entropy; generating partitions; σ-algebras symbolization; KS entropy; generating partitions; σ-algebras

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Stolz, I.; Keller, K. A General Symbolic Approach to Kolmogorov-Sinai Entropy. Entropy 2017, 19, 675.

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