Slopes of 3-dimensional Subshifts of Finite Type

Etienne Moutot; Pascal Vanier

doi:10.1007/978-3-319-90530-3_22

paper

Slopes of 3-dimensional Subshifts of Finite Type

arXiv:1806.07101 · doi:10.1007/978-3-319-90530-3_22

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 $Σ_{2}^{0}$ set may be realized as a a set of slopes of an SFT.

12 pages, published in CSR 2018