| Abstract: |
| There has been a lot of study on substitution tilings with finite local complexity in terms of their dynamical, spectral, and geometric properties. However very little is known for substitution tilings with infinite local complexity and it is getting more attention. We develop a sufficient condition for the substitution dynamical system to be uniquely ergodic. The unique ergodicity on substitution dynamical system has been developed already in [Frank-Sadun `14] and [Frettloh-Richard `14]. But we find a concrete measure of cylinder sets and it is used to make a connection to dynamical and spectral properties of substitution tilings. As a result, we find four equivalent properties for the substitution dynamical systems to be not weakly mixing. |
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