When size matters: subshifts and their related tiling spaces

DOI10.1017/S0143385702001633zbMath1042.37008arXivmath/0201152OpenAlexW2963225454MaRDI QIDQ4437756

Lorenzo Sadun, Alex Clark

Publication date: 3 December 2003

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0201152

zbMATH Keywords

conjugacyweakly mixingsubstitution shifts

Mathematics Subject Classification ID

Related Items (34)

Preface to the special issue on the Pisot substitution conjecture ⋮ Pair correlations of aperiodic inflation rules via renormalisation: some interesting examples ⋮ Finitely balanced sequences and plasticity of 1-dimensional tilings ⋮ Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to \(\beta\)-shifts ⋮ Diffraction of compatible random substitutions in one dimension ⋮ Multidimensional continued fractions and symbolic codings of toral translations ⋮ Geometry, dynamics, and arithmetic of $S$-adic shifts ⋮ Self-similarity and spectral theory: on the spectrum of substitutions ⋮ Algorithm for determining pure pointedness of self-affine tilings ⋮ Uniformly distributed orbits in \(\mathbb{T}^d\) and singular substitution dynamical systems ⋮ The Cech cohomology and the spectrum for 1-dimensional tiling systems ⋮ On ergodic averages for parabolic product flows ⋮ Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings ⋮ On the modulus of continuity for spectral measures in substitution dynamics ⋮ Substitutions, tiling dynamical systems and minimal self-joinings ⋮ Introduction to Hierarchical Tiling Dynamical Systems ⋮ Renormalisation of Pair Correlations and Their Fourier Transforms for Primitive Block Substitutions ⋮ Yet Another Characterization of the Pisot Substitution Conjecture ⋮ The mapping class group of a minimal subshift ⋮ Diffraction intensities of a class of binary Pisot substitutions via exponential sums ⋮ The Pisot conjecture for -substitutions ⋮ The homology core of matchbox manifolds and invariant measures ⋮ The cohomological equation over dynamical systems arising from Delone sets ⋮ Geometrical models for a class of reducible Pisot substitutions ⋮ Tiling deformations, cohomology, and orbit equivalence of tiling spaces ⋮ A primer of substitution tilings of the Euclidean plane ⋮ A spectral cocycle for substitution systems and translation flows ⋮ Pattern equivariant cohomology and theorems of Kesten and Oren ⋮ Rotation numbers and rotation classes on one-dimensional tiling spaces ⋮ Fusion: a general framework for hierarchical tilings of \(\mathbb{R }^d\) ⋮ A combinatorial approach to products of Pisot substitutions ⋮ Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction ⋮ Conjugacies for tiling dynamical systems ⋮ Pure discrete spectrum for a class of one-dimensional substitution tiling systems

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