**Title:** Automorphisms and ergodic measures for subshifts with low factor complexity

**Speaker:** Van Cyr

**Speaker Info:** Bucknell University

**Brief Description:**

**Special Note**: **Unusual time**

**Abstract:**

The automorphism group of a symbolic dynamical system (X,sigma) is the group of homeomorphisms of X that commute with sigma. For many natural systems, this group is extremely large and complicated (e.g. a theorem of Boyle, Lind, and Rudloph shows that if X is a topologically mixing SFT, then Aut(X) contains isomorphic copies of all finite groups, the free group on two generators, and the direct sum of countably many copies of Z). This can be interpreted as a manifestation of the ``high complexity'' of these shifts.In this talk I will discuss recent joint work with B. Kra which places restrictions on the automorphism group of any topologically transitive subshift (not necessarily an SFT) of ``low complexity.'' This class contains the Sturmian shifts, the Rauzy-Arnoux shifts, any other transitive subshift whose factor complexity function grows subquadratically. One of our main results is that, for these shifts, if $H$ is the subgroup of Aut(X) generated by sigma then\Aut(X)/H is a periodic group.

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