Adamczewski Boris
On powers of words occurrung in binary coding of rotations.
We discuss combinatorial properties of a class of binary sequences
generalizing Sturmian sequences and obtained as a coding of an
irrational rotation on the circle with respect to a partition in two
intervals. We give a characterization of those having a finite index in
terms of their ${\cal D}$expansion. Then, we deal with powers occurring
at the begining of these words and we prove, contrary to the Sturmian case,
the existence of such sequences without any asymptotic initial power.
We keep on this study by showing that all charateristic sequences have
even so almost initial powers and we apply this property to obtain the
transcendence of associated continued fractions.
