A note on univoque self-Sturmian numbers

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 in (1, 2) is univoque and self-Sturmian if and only if the -expansion of 1 is of the form 1v, where

• Type: Journal
• Year: 2008
• Where: ITA
• Authors: Jean-Paul Allouche
• Keywords: Communications, ITA 2008, Real Number, Unimodal Continuous Maps, Univoque Real Numbers