• Corpus ID: 222133858

Invariant sets and nilpotency of endomorphisms of algebraic sofic shifts

@article{CeccheriniSilberstein2020InvariantSA,
  title={Invariant sets and nilpotency of endomorphisms of algebraic sofic shifts},
  author={Tullio Ceccherini-Silberstein and Michel Coornaert and Xuan Kien Phung},
  journal={arXiv: Dynamical Systems},
  year={2020}
}
Let $G$ be a group and let $V$ be an algebraic variety over an algebraically closed field $K$. Let $A$ denote the set of $K$-points of $V$. We introduce algebraic sofic subshifts $\Sigma \subset A^G$ and study endomorphisms $\tau \colon \Sigma \to \Sigma$. We generalize several results for dynamical invariant sets and nilpotency of $\tau$ that are well known for finite alphabet cellular automata. Under mild assumptions, we prove that $\tau$ is nilpotent if and only if its limit set, i.e., the… 

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