### 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.Full Text: PDF PostScript