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Substitutions, tiling dynamical systems and minimal self-joinings

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  • We investigate substitution subshifts and tiling dynamical systems arising from the substitutions (1) $\theta: 0 \rightarrow 001, 1 \rightarrow 11001$ and (2) $\eta: 0 \rightarrow 001, 1 \rightarrow 11100$. We show that the substitution subshifts arising from $\theta$ and $\eta$ have minimal self-joinings and are mildly mixing. We also give a criterion for 1-dimensional tiling systems arising from $\theta$ or $\eta$ to have minimal self-joinings. We apply this to obtain examples of mildly mixing 1-dimensional tiling systems.
    Mathematics Subject Classification: Primary: 37A25, 37B10; Secondary: 52C23.


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