The automorphism group of a minimal shift of stretched exponential growth

Abstract

The group of automorphisms of a symbolic dynamical system is countable, butoften 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 highlyconstrained. 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.

Locations

• arXiv (Cornell University) - View - PDF
• Journal of Modern Dynamics - View - PDF