Abstract
Two finite words u and v are called Abelian equivalent if each letter occurs equally many times in both u and v . The abelian closure A ( x ) of (the shift orbit closure of) an infinite word x is the set of infinite words y such that, for each factor u of y , there exists a factor v of x which is abelian equivalent to u . The notion of an abelian closure gives a characterization of Sturmian words: among binary uniformly recurrent words, Sturmian words are exactly those words for which A ( x ) equals the shift orbit closure Ω ( x ) . In this paper we show that, contrary to larger alphabets, the abelian closure of a uniformly recurrent aperiodic binary word which is not Sturmian contains infinitely many minimal subshifts.
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