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The group of automorphisms of a symbolic dynamical system is countable, butoften very large. For example, for a mixing subshift of finite type, theautomorphism group contains isomorphic copies of the free group on twogenerators and the direct sum of countably many copies of $\mathbb{Z}$. Incontrast, the group of automorphisms of a symbolic system of zero entropy seemsto be highly constrained. Our main result is that the automorphism group of anyminimal subshift of stretched exponential growth with exponent $<1/2$, isamenable (as a countable discrete group). For shifts of polynomial growth, wefurther show that any finitely generated, torsion free subgroup of Aut(X) isvirtually nilpotent.

The automorphism group of a minimal shift of stretched exponential growth