Polygonal Z2‐subshifts. Issue 2 (19th March 2020)

• Record Type: Journal Article
• Authors: Franks, John; Kra, Bryna
• Is Part Of: Proceedings of the London Mathematical Society. Volume 121:Issue 2(2020)
• Page Start: 252
• Page End: 286
• Publication Date: 2020-03-19
• Subjects: 37B10 -- 37B15 -- 37B40 -- 37B50 (primary); Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms.12313
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract: Let P ⊂ Z 2 be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex v ∈ P is uniquely determined by the labeling of all other points in the polygon. We introduce a class of Z 2 ‐shift systems, the polygonal shifts, determined by such a polygon: These are shift systems such that the restriction of any x ∈ X to some polygon P has this property. These polygonal systems are related to various well‐studied classes of shift systems, including subshifts of finite type and algebraic shifts, but also many other systems. We give necessary conditions for a Z 2 ‐system X to be polygonal, in terms of the nonexpansive subspaces of X, and under further conditions can give a complete characterization for such systems.