Locally periodic infinite words and a chaotic behaviour.

We call a one-way infinite word w over a finite alphabet (ρ,ρ)-repetitive if all long enough prefixes of w contain as a suffix a repetition of order ρ of a word of length at most p. We show that each (2,4)-repetitive word is ultimately periodic, as well as that there exist nondenumerably many, and hence also nonultimately periodic, (2,5)-repetitive words. Further we characterize nonultimately periodic (2, 5)-repetitive words both structurally and algebraically. [ABSTRACT FROM AUTHOR]