Codings of rotations and continued fractions
It is well-known that the classical continued fraction algorithm describes a generating process by help of morphisms for Sturmian sequences [see for instance \textit{P. Arnoux} and \textit{G. Rauzy}, Bull. Soc. Math. Fr. 119, 199-215 (1991; Zbl 0789.28011)]. The aim of the paper under review is to extend this result to binary codings of rotations: such a sequence is defined as the coding of the orbit under an irrational rotation of a point on the 1-dimensional torus divided into two intervals (in the Sturmian case, the length of one interval equals the rotation angle). If the lengths of both intervals of the partition are larger than the rotation angle, then it is proved that the set of factors of any binary coding (under this partition) is generated by the iteration of four particular morphisms. Moreover, the continued-fraction-like algorithm which describes the iterations ordering is explicitly given. Note that it remains to explore the connections between this algorithm and some other classical algorithms defined as a skew product of the continued fraction transformation, as for instance in [\textit{Y. Hara-Mimachi} and \textit{S. Ito}, Tokyo J. Math. 14, 251-267 (1991; Zbl 0751.11034)].
scientific article; zbMATH DE number 1236184