On the Lyndon Dynamical Systems
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 (-β)-expansion of -ββ + 1 for some β> 1.
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