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arXiv · 2112.07094

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

Omer Tamuz
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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.

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Omer Tamuz. 2021-12-14. Homomorphisms to $\mathbb{R}$ of automorphism groups of zero entropy shifts. https://arxiv.org/abs/2112.07094

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