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