Next Article in Journal
Automated Detection of Paroxysmal Atrial Fibrillation Using an Information-Based Similarity Approach
Next Article in Special Issue
An Operation Reduction Using Fast Computation of an Iteration-Based Simulation Method with Microsimulation-Semi-Symbolic Analysis
Previous Article in Journal
Maximum Exergetic Efficiency Operation of a Solar Powered H2O-LiBr Absorption Cooling System
Previous Article in Special Issue
Characterisation of the Effects of Sleep Deprivation on the Electroencephalogram Using Permutation Lempel–Ziv Complexity, a Non-Linear Analysis Tool
Open AccessArticle

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)
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
Show Figures

Figure 1

MDPI and ACS Style

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

AMA Style

Stolz I, Keller K. A General Symbolic Approach to Kolmogorov-Sinai Entropy. Entropy. 2017; 19(12):675.

Chicago/Turabian Style

Stolz, Inga; Keller, Karsten. 2017. "A General Symbolic Approach to Kolmogorov-Sinai Entropy" Entropy 19, no. 12: 675.

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Search more from Scilit
Back to TopTop