https://hal.inria.fr/hal-00990432Salimov, Pavel VadimovichPavel VadimovichSalimovSobolev Institute of Mathematics - SB RAS - Siberian Branch of the Russian Academy of SciencesOn uniform recurrence of a direct productHAL CCSD2010infinite wordsuniform recurrencestrong recurrencesymmetric morphismsThue-Morse word[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Inria Sophia Antipolis-MÃ©diterranÃ©e / I3s, Service Ist2014-05-13 15:36:482017-10-14 01:04:012014-05-13 16:00:52enJournal articleshttps://hal.inria.fr/hal-00990432/document10.46298/dmtcs.522application/pdf1The 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.