Biinfinite words with maximal recurrent unbordered factors

A finite non-empty word z is said to be a border of a finite non-empty word w if w=uz=zv for some non-empty words u and v. A finite non-empty word is said to be bordered if it admits a border, and it is said to be unbordered otherwise. In this paper, we give two characterizations of the biinfinite words of the form ...uuuvuuu..., where u and v are finite words, in terms of its unbordered factors. The main result of the paper states that the words of the form ...uuuvuuu... are precisely the biinfinite words w=...a_{-2}a_{-1}a_0a_1a_2... for which there exists a pair (l_0,r_0) of integers with l_0