# American Institute of Mathematical Sciences

2016, 10: 483-495. doi: 10.3934/jmd.2016.10.483

## The automorphism group of a minimal shift of stretched exponential growth

 1 Department of Mathematics, Bucknell University, 1 Dent Drive, Lewisburg, PA 17837, United States 2 Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, United States

Received  September 2015 Revised  August 2016 Published  October 2016

The group of automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the automorphism group contains isomorphic copies of the free group on two generators and the direct sum of countably many copies of $\mathbb{Z}$. In contrast, the group of automorphisms of a symbolic system of zero entropy seems to be highly constrained. Our main result is that the automorphism group of any minimal subshift of stretched exponential growth with exponent $<1/2$, is amenable (as a countable discrete group). For shifts of polynomial growth, we further show that any finitely generated, torsion free subgroup of Aut(X) is virtually nilpotent.
Citation: Van Cyr, Bryna Kra. The automorphism group of a minimal shift of stretched exponential growth. Journal of Modern Dynamics, 2016, 10: 483-495. doi: 10.3934/jmd.2016.10.483
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