Exact renormalisation equations yield the relative frequency of any patch in a primitive substitution tiling, with transfer to symbolic and other suspension systems.
When size matters: subshifts and their related tiling spaces
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abstract
We investigate the dynamics of substitution subshifts and their associated tiling spaces. For a given subshift, the associated tiling spaces are all homeomorphic, but their dynamical properties may differ. We give criteria for such a tiling space to be weakly mixing, and for the dynamics of two such spaces to be topologically conjugate.
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Exact renormalisation for patch frequencies in inflation systems
Exact renormalisation equations yield the relative frequency of any patch in a primitive substitution tiling, with transfer to symbolic and other suspension systems.