Homomorphisms to \ℝ of automorphism groups of zero entropy\n shifts

2021/12/13 by Omer Tamuz, Tamuz, Omer
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2112.07094

openalex publication_date 2021/12/13 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We show that the automorphism group of every zero entropy infinite shift\nadmits a "drift" homomorphism to (\ℝ,+) that maps the shift map to 1.\nThis homomorphism arises as the expectation, under an invariant measure, of a\ncocycle defined on a space of asymptotic pairs.\n

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