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

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  • Philippe Leroux

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.

Suggested Citation

  • Philippe Leroux, 2005. "Coassociative grammar, periodic orbits, and quantum random walk over ℤ," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-18, January.
    • Handle: RePEc:hin:jijmms:782735
    DOI: 10.1155/IJMMS.2005.3979
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