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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Hindawi Limited
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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doaj-f6f1f989282e434bb59cc5fa43cc7bc92020-11-24T23:35:20ZengHindawi LimitedInternational 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Philippe Leroux |
| spellingShingle |
Philippe Leroux Coassociative grammar, periodic orbits, and quantum random walk over ℤ International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Philippe Leroux |
| author_sort |
Philippe Leroux |
| title |
Coassociative grammar, periodic orbits, and quantum random
walk over ℤ |
| title_short |
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_sort |
coassociative grammar, periodic orbits, and quantum random
walk over ℤ |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2005-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/IJMMS.2005.3979 |
| work_keys_str_mv |
AT philippeleroux coassociativegrammarperiodicorbitsandquantumrandomwalkoverz |
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1725526512425238528 |