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Baake, Michael; Roberts, John A. G. and Yassawi, Reem
(2018).
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 ℤd-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
- Depositing User
- Reem Yassawi