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Substitutions, tiling dynamical systems and minimal self-joinings
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
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