REVERSING AND EXTENDED SYMMETRIES OF SHIFT SPACES

Baake M, Roberts JAG, Yassawi R (2018)
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 38(2): 835-866.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Baake, MichaelUniBi; Roberts, John A. G.; Yassawi, Reem
Abstract / Bemerkung
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.
Stichworte
Symbolic dynamics; substitutions; shift spaces; tiling dynamics; automorphism and symmetry groups; reversibility; extended symmetries
Erscheinungsjahr
2018
Zeitschriftentitel
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Band
38
Ausgabe
2
Seite(n)
835-866
ISSN
1078-0947
eISSN
1553-5231
Page URI
https://pub.uni-bielefeld.de/record/2917039

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Baake M, Roberts JAG, Yassawi R. REVERSING AND EXTENDED SYMMETRIES OF SHIFT SPACES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. 2018;38(2):835-866.
Baake, M., Roberts, J. A. G., & Yassawi, R. (2018). REVERSING AND EXTENDED SYMMETRIES OF SHIFT SPACES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 38(2), 835-866. https://doi.org/10.3934/dcds.2018036
Baake, M., Roberts, J. A. G., and Yassawi, R. (2018). REVERSING AND EXTENDED SYMMETRIES OF SHIFT SPACES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 38, 835-866.
Baake, M., Roberts, J.A.G., & Yassawi, R., 2018. REVERSING AND EXTENDED SYMMETRIES OF SHIFT SPACES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 38(2), p 835-866.
M. Baake, J.A.G. Roberts, and R. Yassawi, “REVERSING AND EXTENDED SYMMETRIES OF SHIFT SPACES”, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 38, 2018, pp. 835-866.
Baake, M., Roberts, J.A.G., Yassawi, R.: REVERSING AND EXTENDED SYMMETRIES OF SHIFT SPACES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. 38, 835-866 (2018).
Baake, Michael, Roberts, John A. G., and Yassawi, Reem. “REVERSING AND EXTENDED SYMMETRIES OF SHIFT SPACES”. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 38.2 (2018): 835-866.

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