Thue-Morse-Sturmian words and critical bases for ternary alphabets

2019/02/19 by Wolfgang Steiner, Steiner, Wolfgang · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.1902.07078

arxiv created 2019/02/19 · arxiv updated 2019/02/20

Abstract

The set of unique β-expansions over the alphabet \0,1\ is trivial for β below the golden ratio and uncountable above the Komornik-Loreti constant. Generalisations of these thresholds for three-letter alphabets were studied by Komornik, Lai and Pedicini (2011, 2017). We use S-adic words including the Thue-Morse word (which defines the Komornik-Loreti constant) and Sturmian words (which characterise generalised golden ratios) to determine the value of a certain generalisation of the Komornik-Loreti constant to three-letter alphabets.

Cited by

• Topology of univoque sets in double-base expansions

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• Critical bases for ternary alphabets
• Generalized golden ratios of ternary alphabets
• Circular critical exponents for Thue-Morse factors
• Critical exponents of infinite balanced words
• On a family of continued fractions in Q((T¹)) associated to infinite binary words derived from the Thue-Morse sequence