Generalized $\beta$-expansions, substitution tilings, and local finiteness

DOI10.1090/S0002-9947-07-04527-8zbMath1138.37010arXivmath/0506098OpenAlexW2081361698MaRDI QIDQ5437591

E. Arthur jun. Robinson, Natalie Priebe Frank

Publication date: 21 January 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506098

zbMATH Keywords

Pisot numberlocally finite tilingtiling substitution

Mathematics Subject Classification ID

Related Items (18)

Fibonacci direct product variation tilings ⋮ Discrepancy and rectifiability of almost linearly repetitive Delone sets ⋮ Tilings associated with non-Pisot matrices ⋮ Second-order ergodic theorem for self-similar tiling systems ⋮ Small cocycles, fine torus fibrations, and a \({\mathbb {Z}^{2}}\) subshift with neither ⋮ Dynamical properties of almost repetitive Delone sets ⋮ On substitution tilings and Delone sets without finite local complexity ⋮ Limit theorems for self-similar tilings ⋮ The Cech cohomology and the spectrum for 1-dimensional tiling systems ⋮ Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings ⋮ Delone Sets and Dynamical Systems ⋮ Introduction to Hierarchical Tiling Dynamical Systems ⋮ Renormalisation of Pair Correlations and Their Fourier Transforms for Primitive Block Substitutions ⋮ Beta-expansions, natural extensions and multiple tilings associated with Pisot units ⋮ A primer of substitution tilings of the Euclidean plane ⋮ Three variations on a theme by Fibonacci ⋮ Fusion: a general framework for hierarchical tilings of \(\mathbb{R }^d\) ⋮ Pure point spectrum and regular model sets in substitution tilings on \(\mathbb{R}^d\)

Cites Work

• Rigidity of planar tilings
• Some generalizations of the pinwheel tiling
• Representations for real numbers and their ergodic properties
• On Periodic Expansions of Pisot Numbers and Salem Numbers
• Ergodic properties of a class of piecewise linear transformations
• Dynamics of self-similar tilings
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• Unnamed Item

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