Substitutions, tiling dynamical systems and minimal self-joinings

We investigate substitution subshifts and tiling dynamical systems arising from the substitutions (1) θ: 0 \rightarrow 001,1 \rightarrow 11001 and (2) η: 0 \rightarrow 001,1 \rightarrow 11100. We show that the substitution subshifts arising from θand ηhave minimal self-joinings and are mildly mixing. We also give a criterion for 1-dimensional tiling systems arising from θor ηto have minimal self-joinings. We apply this to obtain examples of mildly mixing 1-dimensional tiling systems.

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