On the Lyndon dynamical system (Q281895)

Lyndon systems are defined as symbolic dynamical systems where all (shifted) words are larger than or equal to a given word, which is itself a weak Lyndon word, i.e., larger than or equal to all its suffixes. Here, words are ordered by the alternate order, and the dynamical systems are closely related to negative beta-shifts. The author characterizes when such a system has positive entropy. He also gives a new proof for a result of the reviewer [Acta Math. Hung. 139, No. 1--2, 106--119 (2013; Zbl 1291.11019)] on the characterization of \((-\beta)\)-expansions of \(-\beta/(\beta+1)\).