Reversing and extended symmetries of shift spaces

Baake, Michael; Roberts, John A. G. and Yassawi, Reem (2018). Reversing and extended symmetries of shift spaces. Discrete & Continuous Dynamical Systems - Series A, 38(2) pp. 835–866.

DOI: https://doi.org/10.3934/dcds.2018036

Abstract

The reversing symmetry group is considered in the setting of symbolic dynamics. While this group is generally too big to be analysed in detail, there are interesting cases with some form of rigidity where one can determine all symmetries and reversing symmetries explicitly. They include Sturmian shifts as well as classic examples such as the Thue–Morse system with various generalisations or the Rudin–Shapiro system. We also look at generalisations of the reversing symmetry group to higher-dimensional shift spaces, then called the group of extended symmetries. We develop their basic theory for faithful ℤ^d-actions, and determine the extended symmetry group of the chair tiling shift, which can be described as a model set, and of Ledrappier’s shift, which is an example of algebraic origin.

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About

• Item ORO ID
• 67275
• Item Type
• Journal Item
• ISSN
• 1078-0947
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Not Set	Not Set	Australian Research Council
  Not Set	CRC 701	German Research Foundation

• Keywords
• symbolic dynamics; substitutions; shift spaces; tiling dynamics; automorphism and symmetry groups; reversibility; extended symmetries
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Related URLs
• • https://arxiv.org/abs/1611.05756(Other)
• Depositing User
• Reem Yassawi