Coassociative grammar, periodic orbits, and quantum random walk over ℤ

Philippe Leroux

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-18

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 ↦ 2 x mod ⁡ 1 , x ∈ [ 0 , 1 ] , are also given.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:782735

DOI: 10.1155/IJMMS.2005.3979

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