A Garden of Eden theorem for linear subshifts

Details A Garden of Eden theorem for linear subshifts A Garden of Eden theorem for linear subshifts

2010-02-21

arxiv.org/abs/1002.3957v1

Ergod. Th. & Dynam. Sys. 32 (2012), 81-102

Mathematics

Dynamical Systems

Scientific paper

Let $G$ be an amenable group and let $V$ be a finite-dimensional vector space over an arbitrary field $\K$. We prove that if $X \subset V^G$ is a strongly irreducible linear subshift of finite type and $\tau \colon X \to X$ is a linear cellular automaton, then $\tau$ is surjective if and only if it is pre-injective. We also prove that if $G$ is countable and $X \subset V^G$ is a strongly irreducible linear subshift, then every injective linear cellular automaton $\tau \colon X \to X$ is surjective.

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