A1 Refereed original research article in a scientific journal
On pointwise periodicity in tilings, cellular automata, and subshifts
Authors: Meyerovitch T, Salo V
Publisher: EUROPEAN MATHEMATICAL SOC
Publication year: 2019
Journal: Groups, Geometry, and Dynamics
Journal name in source: GROUPS GEOMETRY AND DYNAMICS
Journal acronym: GROUP GEOM DYNAM
Volume: 13
Issue: 2
First page : 549
Last page: 578
Number of pages: 30
ISSN: 1661-7207
eISSN: 1661-7215
DOI: https://doi.org/10.4171/GGD/497
Abstract
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.
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.
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