Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon Theorem

Abstract

We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; vertex-transitive graphs, in particular, Cayley graphs, acted on by automorphisms; groups acting on themselves by multiplication; and integer lattices acted on by translations.

References in corpus (4)

• Sliding block codes between shift spaces over infinite alphabets
• Cellular automata on a $G$-set
• A note on the definition of sliding block codes and the Curtis-Hedlund-Lyndon Theorem
• Right Amenable Left Group Sets and the Tarski-Følner Theorem

Cited by in corpus (5)

• Right Amenable Left Group Sets and the Tarski-Følner Theorem
• Right Amenability And Growth Of Finitely Right Generated Left Group Sets
• Differentiable cellular automata
• The Garden of Eden Theorem for Cellular Automata on Group Sets
• The Moore and the Myhill Property For Strongly Irreducible Subshifts Of Finite Type Over Group Sets