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 | American English |
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Pages (from-to) | 549-578 |
Number of pages | 30 |
Journal | Groups, Geometry, and Dynamics |
Volume | 13 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jan 2019 |
Keywords
- Expansiveness
- Subshifts
- Tilings
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Discrete Mathematics and Combinatorics