Characterization of repetitions in Sturmian words: A new proof

• We provide a new, short proof of characterization of powers in Sturmian words.
• Opposed to previous approaches, we use continued fractions extensively.
• Our approach is more geometric and avoids tricky word combinatorial arguments.
• We obtain a known formula for the fractional index of Sturmian words as a consequence.

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 [6]. 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.