Slopes of 3-dimensional subshifts of finite type

DOI10.1007/978-3-319-90530-3_22zbMATH Open1440.37026arXiv1806.07101OpenAlexW2800348404MaRDI QIDQ1625176

Pascal Vanier, Etienne Moutot

Publication date: 28 November 2018

Abstract: In this paper we study the directions of periodicity of three-dimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction, the slope being the angle of the periodicity vectors. In this paper, we prove that any $Sigm{a}_2^0$ set may be realized as a a set of slopes of an SFT.

Full work available at URL: https://arxiv.org/abs/1806.07101

zbMATH Keywords

subshifts of finite typedirections of periodicityperiodicity vector

Mathematics Subject Classification ID

Symbolic dynamics (37B10) Multidimensional shifts of finite type (37B51)

Related Items (3)

Aperiodic points in $\mathbb Z^2$-subshifts ⋮ Slopes of multidimensional subshifts ⋮ A subshift of finite type in the Takens-Bogdanov bifurcation with \(D_3\) symmetry

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