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arXiv 2011.015242020-11-11math.DScs.ITmath.COmath.GRmath.IT

Shadowing for families of endomorphisms of generalized group shifts

Xuan Kien Phung

备注：: arXiv admin note: text overlap with arXiv:2010.04035
发表信息：: Discrete Contin Dyn Syst Ser A (2022), 42 (1) : 285-299
DOI：: 10.3934/dcds.2021116

英文摘要：

Let $G$ be a countable monoid and let $A$ be an Artinian group (resp. an Artinian module). Let $Σ\subset A^G$ be a closed subshift which is also a subgroup (resp. a submodule) of $A^G$. Suppose that $Γ$ is a finitely generated monoid consisting of pairwise commuting cellular automata $Σ\to Σ$ that are also homomorphisms of groups (resp. homomorphisms of modules) with monoid binary operation given by composition of maps. We show that the valuation action of $Γ$ on $Σ$ satisfies a natural intrinsic shadowing property. Generalizations are also established for families of endomorphisms of admissible group subshifts.

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