International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3979-3996
doi:10.1155/IJMMS.2005.3979
Coassociative grammar, periodic orbits, and quantum random
walk over ℤ
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.
Abstract
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.