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The Garden of Eden theorem for linear cellular automata

  • TULLIO CECCHERINI-SILBERSTEIN (a1) and MICHEL COORNAERT (a2)
Abstract

Let V be a finite-dimensional vector space over a field ${\mathbb{K}}$ and let G be a countable amenable group. Let $\tau \colon V^G \to V^G$ be a linear cellular automaton. We prove that $\tau$ is surjective if and only if it is pre-injective.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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