Glider Automorphisms on Some Shifts of Finite Type and a Finitary Ryan’s Theorem

Abstract : For any mixing SFT X containing a fixed point we construct a reversible shift-commuting continuous map (automorphism) which breaks any given finite point of the subshift into a finite collection of gliders traveling into opposing directions. As an application we show that the automorphism group $${{\mathrm{Aut}}}(X)$$ contains a two-element subset S whose centralizer consists only of shift maps.
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Johan Kopra. Glider Automorphisms on Some Shifts of Finite Type and a Finitary Ryan’s Theorem. 24th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2018, Ghent, Belgium. pp.88-99, ⟨10.1007/978-3-319-92675-9_7⟩. ⟨hal-01824877⟩

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