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Joining properties of automorphisms disjoint with all ergodic systems

2024/12/27 by Przemysław Berk, PRZEMYSŁAW BERK, MARTYNA GÓRSKA +2
Computer Science · Mathematics · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.1017/etds.2024.129

openalex publication_date 2024/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

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

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