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REVERSING AND EXTENDED SYMMETRIES OF SHIFT SPACES

机译：移位空间的反转和扩展对称

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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.
机译：在符号动力学设置中考虑反向对称组。虽然该组通常太大而无法详细分析，但有些有趣的情况具有某种形式的刚度，可以确定所有对称性并明确地反转对称性。它们包括Sturmian移位以及经典示例，例如具有各种概括的Thue-Morse系统或Rudin-Shapiro系统。我们还研究了反向对称群到高维移位空间的一般化，然后将其称为扩展对称群。我们发展了他们忠实的Z〜d动作的基本理论，并确定了椅子平铺移位的对称性扩展组（可以描述为模型集）和Ledrappier移位的对称性组（这是代数起源的一个例子）。

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