SUBSTITUTIONS, TILING DYNAMICAL SYSTEMS AND MINIMAL SELF-JOININGS

Abstract

We investigate substitution subshifts and tiling dynamical systems arising from the substitutions (1) theta : 0 -> 001, 1 -> 11001 and (2) eta : 0 > 001, 1 -> 11100. We show that the substitution subshifts arising from 61 and n have minimal self-joinings and are mildly mixing. We also give a criterion for 1-dimensional tiling systems arising from 61 or n to have minimal self-joinings. We apply this to obtain examples of mildly mixing 1-dimensional tiling systems.