A note on univoque self-Sturmian numbers

CNRS, LRI, UMR 8623, Université Paris Sud, Bâtiment 490, 91405 Orsay Cedex, France; allouche@lri.fr

Received: 12 January 2007
Accepted: 22 November 2007

Abstract

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.