4 research outputs found
Extremal properties of (epi)Sturmian sequences and distribution modulo 1
Starting from a study of Y. Bugeaud and A. Dubickas (2005) on a question in
distribution of real numbers modulo 1 via combinatorics on words, we survey
some combinatorial properties of (epi)Sturmian sequences and distribution
modulo 1 in connection to their work. In particular we focus on extremal
properties of (epi)Sturmian sequences, some of which have been rediscovered
several times
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 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