On pointwise periodicity in tilings, cellular automata, and subshifts

Tom Meyerovitch; Ville Salo

doi:10.4171/GGD/497

On pointwise periodicity in tilings, cellular automata, and subshifts

Tom Meyerovitch, Ville Salo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English
Pages (from-to)	549-578
Number of pages	30
Journal	Groups, Geometry, and Dynamics
Volume	13
Issue number	2
DOIs	https://doi.org/10.4171/GGD/497
State	Published - 1 Jan 2019

Keywords

Expansiveness
Subshifts
Tilings

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.4171/GGD/497

Cite this

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AB - 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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KW - Tilings

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On pointwise periodicity in tilings, cellular automata, and subshifts

Abstract

Keywords

ASJC Scopus subject areas

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