Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation point
This paper aims to make further contributions to the exploration of the symbolic dynamics generated by the logistic map at Feigenbaum accumulation point. In particular we are interested in the grammar of these sequences; completing earlier studies we study here arbitrary partitions also. Our main ai...
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | Discrete Dynamics in Nature and Society |
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| Online Access: | http://dx.doi.org/10.1155/S1026022698000168 |
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| _version_ | 1832545668905828352 |
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| author | Werner Ebelings Katja Rateitschak |
| author_facet | Werner Ebelings Katja Rateitschak |
| author_sort | Werner Ebelings |
| collection | DOAJ |
| description | This paper aims to make further contributions to the exploration of the symbolic dynamics generated by the logistic map at Feigenbaum accumulation point. In particular we are interested in the grammar of these sequences; completing earlier studies we study here arbitrary partitions also. Our main aim is the investigation of the special grammars which characterize the long-range correlations between letters. Considering these sequences as standard examples of a complex system, we introduce and discuss a complexity function derived from the conditional entropies. Further we discuss local predictabilities. |
| format | Article |
| id | doaj-art-bc2f8db113f14d7d89ac90cd859f6ea2 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-bc2f8db113f14d7d89ac90cd859f6ea22025-02-03T07:25:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X1998-01-012318719410.1155/S1026022698000168Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation pointWerner Ebelings0Katja Rateitschak1Institute of Physics, Humboldt University Berlin, Invaliden Str. 110, Berlin D-lOll5, GermanyCenter for Nonlinear Phenomena and Complex Systems, Free University of Brussels, Brussels B-1050, BelgiumThis paper aims to make further contributions to the exploration of the symbolic dynamics generated by the logistic map at Feigenbaum accumulation point. In particular we are interested in the grammar of these sequences; completing earlier studies we study here arbitrary partitions also. Our main aim is the investigation of the special grammars which characterize the long-range correlations between letters. Considering these sequences as standard examples of a complex system, we introduce and discuss a complexity function derived from the conditional entropies. Further we discuss local predictabilities.http://dx.doi.org/10.1155/S1026022698000168Feigenbaum mapShannon entropyComplexity measures. |
| spellingShingle | Werner Ebelings Katja Rateitschak Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation point Discrete Dynamics in Nature and Society Feigenbaum map Shannon entropy Complexity measures. |
| title | Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation point |
| title_full | Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation point |
| title_fullStr | Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation point |
| title_full_unstemmed | Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation point |
| title_short | Symbolic dynamics, entropy and complexity of the feigenbaum map at the accumulation point |
| title_sort | symbolic dynamics entropy and complexity of the feigenbaum map at the accumulation point |
| topic | Feigenbaum map Shannon entropy Complexity measures. |
| url | http://dx.doi.org/10.1155/S1026022698000168 |
| work_keys_str_mv | AT wernerebelings symbolicdynamicsentropyandcomplexityofthefeigenbaummapattheaccumulationpoint AT katjarateitschak symbolicdynamicsentropyandcomplexityofthefeigenbaummapattheaccumulationpoint |