The Automorphism Group of a Shift of Linear Growth: beyond Transitivity
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چکیده
For a finite alphabet A and shift X ⊆ AZ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group Aut(X). For such systems, we show that every finitely generated subgroup of Aut(X) is virtually Zd, in contrast to the behavior when the complexity function grows more quickly. With additional dynamical assumptions we show more: if X is transitive, then Aut(X) is virtually Z; if X has dense aperiodic points, then Aut(X) is virtually Zd. We also classify all finite groups that arise as the automorphism group of a shift.
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تاریخ انتشار 2014