关于Lyndon动力系统
On the Lyndon Dynamical Systems
摘要：
给定一个全有限序字母表$ A $，赋予$ A $上的词集交替的字典序，我们定义了一类新的Lyndon词.我们研究了Lyndon系统的基本性质。将负基β位移与Lyndon系统联系起来，得到了负基β位移的一些基本性质。我们发现，独立于W。Steiner的方法，条件，其中一个字是$(-β)$ -扩展的$-\fracβ{β+ 1} $为一些$ β> 1$。
英文摘要：
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 $-\fracβ{β+ 1} $ for some $ β> 1$.
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