Minimal Self-Joinings, Bounded Constructions, and Weak Closure of Ergodic Actions

2012/12/11 by V. V. Ryzhikov, Ryzhikov, V. V. · 2 citations
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1212.2602

openalex publication_date 2012/12/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For a weakly mixing bounded rank-one construction the disjointness of its powers is proved. For non-rigid constructions we get minimal self-joinings. Examples of non-mixing rank one actions with explicit weak closure are proposed.

Cited by

• Generalized Chacon polynomial constructions
• Chacon's Type Ergodic Transformations with Unbounded Arithmetic Spacers

Related

• Spectral properties and approximations of joinings for infinite rank-one actions
• On ergodic actions whose self-joinings are graphs
• Disjointness between bounded rank-one transformations
• Bounded rank-one transformations
• Self-joinings and generic extensions of ergodic systems