Characterization of repetitions in Sturmian words: A new proof

Abstract

We present a new, dynamical way to study powers (that is, repetitions) in Sturmian words based on results from Diophantine approximation theory. As a result, we provide an alternative and shorter proof of a result by Damanik and Lenz characterizing powers in Sturmian words [Powers in Sturmian sequences, Eur. J. Combin. 24 (2003), 377--390]. Further, as a consequence, we obtain a previously known formula for the fractional index of a Sturmian word based on the continued fraction expansion of its slope.Comment: 9 pages, 1 figur