On Uniform Recurrence of a Direct Product
Pavel Vadimovich Salimov
Abstract
The direct product of two words is a naturally defined word on the
alphabet of pairs of symbols. An infinite word is uniformly
recurrent if each its subword occurs in it with bounded gaps. An
infinite word is strongly recurrent if the direct product of
it with each uniformly recurrent word is also uniformly recurrent. We
prove that fixed points of the expanding binary symmetric morphisms
are strongly recurrent. In particular, such is the Thue-Morse word.
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