Coassociative grammar, periodic orbits, and quantum random walk over ℤ
Inspired by a work of Joni and Rota, we show that the combinatorics generated by a quantisation of the Bernoulli random walk over ℤ can be described from a coassociative coalgebra. Relationships between this coalgebra and the set of periodic orbits of the classical chaotic system x↦2x mod1, x∈[0,...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3979 |
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| _version_ | 1832551573037776896 |
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| author | Philippe Leroux |
| author_facet | Philippe Leroux |
| author_sort | Philippe Leroux |
| collection | DOAJ |
| description | Inspired by a work of Joni and Rota, we show that the
combinatorics generated by a quantisation of the Bernoulli random
walk over ℤ can be described from a coassociative coalgebra. Relationships between this
coalgebra and the set of periodic orbits of the classical chaotic system x↦2x mod1, x∈[0,1], are also given. |
| format | Article |
| id | doaj-art-f6f1f989282e434bb59cc5fa43cc7bc9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f6f1f989282e434bb59cc5fa43cc7bc92025-02-03T06:01:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005243979399610.1155/IJMMS.2005.3979Coassociative grammar, periodic orbits, and quantum random walk over ℤPhilippe Leroux0Institut de Recherche Mathématique, Université de Rennes I and CNRS UMR 6625, Campus de Beaulieu, Rennes Cedex 35042, FranceInspired by a work of Joni and Rota, we show that the combinatorics generated by a quantisation of the Bernoulli random walk over ℤ can be described from a coassociative coalgebra. Relationships between this coalgebra and the set of periodic orbits of the classical chaotic system x↦2x mod1, x∈[0,1], are also given.http://dx.doi.org/10.1155/IJMMS.2005.3979 |
| spellingShingle | Philippe Leroux Coassociative grammar, periodic orbits, and quantum random walk over ℤ International Journal of Mathematics and Mathematical Sciences |
| title | Coassociative grammar, periodic orbits, and quantum random
walk over ℤ |
| title_full | Coassociative grammar, periodic orbits, and quantum random
walk over ℤ |
| title_fullStr | Coassociative grammar, periodic orbits, and quantum random
walk over ℤ |
| title_full_unstemmed | Coassociative grammar, periodic orbits, and quantum random
walk over ℤ |
| title_short | Coassociative grammar, periodic orbits, and quantum random
walk over ℤ |
| title_sort | coassociative grammar periodic orbits and quantum random walk over z |
| url | http://dx.doi.org/10.1155/IJMMS.2005.3979 |
| work_keys_str_mv | AT philippeleroux coassociativegrammarperiodicorbitsandquantumrandomwalkoverz |