Substitutions, tiling dynamical systems and minimal self-joinings

Younghwan Son

doi:10.3934/dcds.2014.34.4855

Article Contents

2014, Volume 34, Issue 11: 4855-4874. Doi: 10.3934/dcds.2014.34.4855

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Substitutions, tiling dynamical systems and minimal self-joinings

Younghwan Son^1,

1.
Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 7610001

Received: August 31, 2013

Revised: February 28, 2014

Published: October 2014

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Abstract

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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Mathematics Subject Classification: Primary: 37A25, 37B10; Secondary: 52C23.

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