International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3979-3996

Coassociative grammar, periodic orbits, and quantum random walk over

Philippe Leroux

Institut de Recherche Mathématique, Université de Rennes I and CNRS UMR 6625, Campus de Beaulieu, Rennes Cedex 35042, France

Received 13 January 2005; Revised 20 September 2005

Copyright © 2005 Philippe Leroux. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Inspired by a work of Joni and Rota, we show that the combinatorics generated by a quantisation of the Bernoulli random walk over can be described from a coassociative coalgebra. Relationships between this coalgebra and the set of periodic orbits of the classical chaotic system x2x mod1, x[0,1], are also given.