On the Lyndon dynamical system
Copyright policy )On the Lyndon dynamical system
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$.
beta-expansion, Combinatorics on words, negative basis, Symbolic dynamics, Lyndon words, Dynamical Systems (math.DS), symbolic dynamical systems, 37B10, 05C99, 11A63, FOS: Mathematics, Mathematics - Dynamical Systems, Radix representation; digital problems
beta-expansion, Combinatorics on words, negative basis, Symbolic dynamics, Lyndon words, Dynamical Systems (math.DS), symbolic dynamical systems, 37B10, 05C99, 11A63, FOS: Mathematics, Mathematics - Dynamical Systems, Radix representation; digital problems
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