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arXiv · 1707.07730

On the Lyndon Dynamical Systems

Florent Nguema Ndong
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Abstract

Given a totally finite ordered alphabet $ A $, endowing the set of words over $ A $ with the alternating lexicographic order, we define a new class of Lyndon words. We study the fundamental properties of the associated symbolic dynamical systems called Lyndon system. We derive some fundamental properties of the beta-shift with negative base by relating it with the Lyndon system. We find, independently of W. Steiner's method, the conditions for which a word is the $(-\beta)$-expansion of $-\frac{\beta}{\beta + 1} $ for some $ \beta> 1$.

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Florent Nguema Ndong. 2017-07-24. On the Lyndon Dynamical Systems. https://arxiv.org/abs/1707.07730

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