When size matters: subshifts and their related tiling spaces

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.

Updated 2018 to version published in 2003. 14 pages, no figures, LaTeX

Cited by in corpus (18)

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• A combinatorial approach to products of Pisot substitutions
• Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings
• Renormalisation of pair correlations and their Fourier transforms for primitive block substitutions
• The Pisot Conjecture for $\beta$-substitutions
• Spectral cocycle for substitution tilings
• Rotation numbers and rotation classes on one-dimensional tiling spaces
• Modulus of continuity for spectral measures of suspension flows over Salem type substitutions
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• When Shape Matters: Deformations of Tiling Spaces
• Absence of absolutely continuous diffraction spectrum for certain S-adic tilings
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• The Mapping Class Group of a Minimal Subshift
• Flow views and infinite interval exchange transformations for recognizable substitutions