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self-sturmian numbers.

RAIRO - Theoretical Informatics and Applications (1)

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A note on univoque self-Sturmian numbers
Jean-Paul Allouche
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 42 / Issue 4 / October 2008

Published online by Cambridge University Press:

04 January 2008, pp. 659-662

Print publication:

October 2008
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We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic Sturmian sequences. As a corollary to our study we obtain that a real number β in (1,2) is univoque and self-Sturmian if and only if the β-expansion of 1 is of the form 1v, where v is a characteristic Sturmian sequence beginning itself in 1.