@article{16746db6cf4443e0a2aee22191264ae9,
title = "On pointwise periodicity in tilings, cellular automata, and subshifts",
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.",
keywords = "Expansiveness, Subshifts, Tilings",
author = "Tom Meyerovitch and Ville Salo",
note = "Funding Information: Acknowledgments. We thank Sebasti{\'a}n Donoso, Fabien Durand, Alejando Maass and Samuel Petite for allowing us to include their currently unpublished Proposition 3.12. We thank Samuel Petite also for pointing out the reference [5]. We thank Alexis Ballier for pointing out that Theorem 1.4 appears in his PhD thesis. We thank the anonymous referee for a careful review and for pointing out a number of corrections. The first author would like to acknowledge support from the People Programme (Marie Curie Actions) of the European Union{\textquoteright}s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 333598 and from the Israel Science Foundation (grant no. 626/14). Publisher Copyright: {\textcopyright} European Mathematical Society.",
year = "2019",
month = jan,
day = "1",
doi = "https://doi.org/10.4171/GGD/497",
language = "English",
volume = "13",
pages = "549--578",
journal = "Groups, Geometry, and Dynamics",
issn = "1661-7207",
publisher = "European Mathematical Society Publishing House",
number = "2",
}