Glider automorphisms and a finitary Ryan’s theorem for transitive subshifts of finite type
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Abstract For any mixing SFT X 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 prove a finitary Ryan’s theorem: the automorphism group $${{\,\mathrm{Aut}\,}}(X)$$ Aut ( X ) contains a two-element subset S whose centralizer consists only of shift maps. We also give an example which shows that a stronger finitary variant of Ryan’s theorem does not hold even for the binary full shift.
2017 ◽
Vol 39
(06)
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pp. 1637-1667
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1990 ◽
Vol 10
(3)
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pp. 421-449
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2009 ◽
Vol 30
(3)
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pp. 809-840
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2016 ◽
Vol 38
(4)
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pp. 1588-1600
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1976 ◽
pp. 117-130
2020 ◽
Vol 32
(7)
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pp. 88-92