On the Lyndon dynamical system

详细信息    查看全文

• 作者：Florent Nguema Ndong ^{florentnn@yahoo.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：37B10 ; 05C99 ; 11A63
• 刊名：Advances in Applied Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：78
• 期：Complete
• 页码：1-26
• 全文大小：404 K

文摘

Given a totally finite ordered alphabet A$\mathcal{A}$, endowing the set of words over A$\mathcal{A}$ with the alternating lexicographic order (see [6]), 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 (see [11]), the conditions for which a word is the (−β)$(-\beta )$-expansion of $-\frac{\beta }{\beta +1}$ for some β>1$\beta >1$.