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We investigate abelian repetitions in Sturmian words. We exploit a bijection between factors of Sturmian words and subintervals of the unitary segment that allows us to study the periods of abelian repetitions by using classical results of elementary Number Theory. We prove that in any Sturmian word the superior limit of the ratio between the maximal exponent of an abelian repetition of period m and m is a number ≥√(5), and the equality holds for the Fibonacci infinite word. We further provearXiv:1209.6013v3 fatcat:3n4lhospzfhptjz7lxc56sdngq