2021/10/03 by Mateusz Więcek, Więcek, Mateusz
Computer Science · Mathematics · #37A35 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 37B40 #Secondary 43A07 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2110.01112
openalex publication_date 2021/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a definition of a \prec-asymptotic pair in a topological action of a countable amenable group G, where \prec is an order on G of type \mathbb Z. We then prove that if (\mathcal O,ν,G) is a multiorder on G, then for every topological G-action of positive entropy there exists an \prec-asympotic pair for almost every order \prec ∈\mathcal O. This result is a generalization of the Blanchard-Host-Ruette Theorem for classical topological dynamical systems (actions of \mathbb Z).