The Open UniversitySkip to content

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.

Full text available as:
PDF (Accepted Manuscript) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (391kB) | Preview
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


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.

Item Type: Journal Item
ISSN: 1078-0947
Project Funding Details:
Funded Project NameProject IDFunding Body
Not SetNot SetAustralian Research Council
Not SetCRC 701German Research Foundation
Keywords: symbolic dynamics; substitutions; shift spaces; tiling dynamics; automorphism and symmetry groups; reversibility; extended symmetries
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:
Item ID: 67275
Depositing User: Reem Yassawi
Date Deposited: 15 Oct 2019 09:14
Last Modified: 13 Nov 2019 13:45
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU