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Joining properties of automorphisms disjoint with all ergodic systems

2023/12/20 by Przemysław Berk, Martyna E. Górska, Berk, Przemysław +3
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2312.13153

openalex publication_date 2023/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the class Erg^⊥ of automorphisms which are disjoint with all ergodic systems. We prove that the identities are the only multipliers of Erg^⊥, that is, each automorphism whose every joining with an element of Erg yields a system which is again an element of Erg, must be an identity. Despite this fact, we show that Erg^⊥ is closed by taking Cartesian products. Finally, we prove that there are non-identity elements in Erg^⊥ whose self-joinings always yield elements in Erg^⊥. This shows that there are non-trivial characteristic classes included in Erg^⊥.

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