A General Symbolic Approach to Kolmogorov-Sinai Entropy
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 bac...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-12-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/19/12/675 |
| _version_ | 1798034562495807488 |
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| author | Inga Stolz Karsten Keller |
| author_facet | Inga Stolz Karsten Keller |
| author_sort | Inga Stolz |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T20:45:57Z |
| format | Article |
| id | doaj.art-15cad4ba874647249f1f8fcc08b475f6 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T20:45:57Z |
| publishDate | 2017-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-15cad4ba874647249f1f8fcc08b475f62022-12-22T04:04:02ZengMDPI AGEntropy1099-43002017-12-01191267510.3390/e19120675e19120675A General Symbolic Approach to Kolmogorov-Sinai EntropyInga Stolz0Karsten Keller1Institute of Mathematics, University of Lübeck, Ratzeburger Allee 160, 23562 Lübeck, GermanyInstitute of Mathematics, University of Lübeck, Ratzeburger Allee 160, 23562 Lübeck, GermanyIt 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.https://www.mdpi.com/1099-4300/19/12/675symbolizationKS entropygenerating partitionsσ-algebras |
| spellingShingle | Inga Stolz Karsten Keller A General Symbolic Approach to Kolmogorov-Sinai Entropy Entropy symbolization KS entropy generating partitions σ-algebras |
| title | A General Symbolic Approach to Kolmogorov-Sinai Entropy |
| title_full | A General Symbolic Approach to Kolmogorov-Sinai Entropy |
| title_fullStr | A General Symbolic Approach to Kolmogorov-Sinai Entropy |
| title_full_unstemmed | A General Symbolic Approach to Kolmogorov-Sinai Entropy |
| title_short | A General Symbolic Approach to Kolmogorov-Sinai Entropy |
| title_sort | general symbolic approach to kolmogorov sinai entropy |
| topic | symbolization KS entropy generating partitions σ-algebras |
| url | https://www.mdpi.com/1099-4300/19/12/675 |
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