English

On the Lyndon Dynamical Systems

Dynamical Systems 2017-07-31 v2

Abstract

Given a totally finite ordered alphabet A A , endowing the set of words over A 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)(-\beta)-expansion of ββ+1-\frac{\beta}{\beta + 1} for some β>1 \beta> 1.

Keywords

Cite

@article{arxiv.1707.07730,
  title  = {On the Lyndon Dynamical Systems},
  author = {Florent Nguema Ndong},
  journal= {arXiv preprint arXiv:1707.07730},
  year   = {2017}
}
R2 v1 2026-06-22T20:56:09.099Z