Glider automorphisms and a finitary Ryan\u2019s theorem for transitive subshifts of finite type

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) 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.