A two-sided sequence over a finite alphabet is uniformly recurrent if every finite word over an alphabet occurring in it occurs with bounded gaps. More precisely, for each such word some ensures that every length- interval contains a complete occurrence. This is equivalent to being a minimal point of the full shift: a finite cover of the orbit closure by preimages of a word's cylinder set bounds its return gaps; conversely, bounded gaps pass to all points of the orbit closure and make every forward orbit dense there. The property concerns finite words, not infinite integer intervals.
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