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arXiv · 1810.02838

Computation of extended symmetry groups for multidimensional subshifts with hierarchical structure

Álvaro Bustos
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Abstract

Automorphism groups are intrincate conjugacy invariants for subshifts, which can reveal important features of the dynamical structure of a shift action. One important case is the study of automorphism groups when the underlying subshift has a very rigid structure, e.g. substitutive subshifts or aperiodic constructions with large-scale self-similarity, such as the Robinson shift. In this work we study the automorphism group of bijective substitutive subshifts, and a potential generalization in the form of the group of extended symmetries, studied previously by Michael Baake, John Roberts and Reem Yassawi (arXiv:1611.05756); these symmetries, by allowing for shearing and other deformations of the underlying group, may reveal additional information of a geometric nature about the structure of these subshifts.

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Álvaro Bustos. 2018-10-05. Computation of extended symmetry groups for multidimensional subshifts with hierarchical structure. https://arxiv.org/abs/1810.02838

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