Shadowing for families of endomorphisms of generalized group shifts

10/31/2020

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by   Xuan Kien Phung, et al.

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Let G be a countable monoid and let A be an Artinian group (resp. an Artinian module). Let Σ⊂ 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→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.