On pointwise periodicity in tilings, cellular automata, and subshifts



: Meyerovitch T, Salo V

Publisher: EUROPEAN MATHEMATICAL SOC

: 2019

: Groups, Geometry, and Dynamics

: GROUPS GEOMETRY AND DYNAMICS

: GROUP GEOM DYNAM

: 13

: 2

: 549

: 578

: 30

: 1661-7207

: 1661-7215

DOI: https://doi.org/10.4171/GGD/497


We study implications of expansiveness and pointwise periodicity for certain groups and semigroups of transformations. Among other things we prove that every pointwise periodic finitely generated group of cellular automata is necessarily finite. We also prove that a subshift over any finitely generated group that consists of finite orbits is finite, and related results for tilings of Euclidean space.



Last updated on 2024-26-11 at 19:48