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 \({{\,\mathrm{Aut}\,}}(X)\) 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.

中文翻译：

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滑模自同构和有限型传递子移位的最终Ryan定理

对于任何混合SFT X，我们都构建了一个可逆的换向换向连续图（自同构），该图将子换挡的任何给定有限点分解为沿相反方向行进的滑翔机的有限集合。作为一个应用，我们证明了最终的Ryan定理：自同构群\（{{\\\ mathrm {Aut} \，}}（X）\）包含一个包含两个元素的子集S，其子集集中仅包含移位图。我们还给出了一个示例，该示例表明即使对于二进制全移位，Ryan定理的更强的最终变式也不成立。