Homomorphisms to $\mathbb{R}$ of automorphism groups of zero entropy shifts

Abstract

We show that the automorphism group of every zero entropy infinite shift admits a "drift" homomorphism to $(\mathbb{R},+)$ that maps the shift map to 1. This homomorphism arises as the expectation, under an invariant measure, of a cocycle defined on a space of asymptotic pairs.

arXiv comment10 pages. Minor corrections with respect to the previous version