Squirals and beyond: substitution tilings with singular continuous spectrum

Baake, Michael and Grimm, Uwe (2014). Squirals and beyond: substitution tilings with singular continuous spectrum. Ergodic Theory and Dynamical Systems, 34(4) pp. 1077–1102.

DOI: https://doi.org/10.1017/etds.2012.191

Abstract

The squiral inflation rule is equivalent to a bijective block substitution rule and leads to an interesting lattice dynamical system under the action of Z². In particular, its balanced version has purely singular continuous diffraction. The dynamical spectrum is of mixed type, with pure point and singular continuous components. We present a constructive proof that admits a generalization to bijective block substitutions of trivial height on Z^d.

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About

• Item ORO ID
• 36994
• Item Type
• Journal Item
• ISSN
• 1469-4417
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2013 Cambridge University Press
• Depositing User
• Uwe Grimm