2018/12/27 by Andrei Alpeev, Alpeev, Andrei, Tom Meyerovitch +3
Computer Science · Mathematics · #37A35 #37B40 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1812.10833
openalex publication_date 2018/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that a topologically predictable action of a countable amenable group has zero topological entropy, as conjectured by Hochman. On route, we investigate invariant random orders and formulate a unified Kieffer-Pinsker formula for the Kolmogorov-Sinai entropy of measure preserving actions of amenable groups. We also present a proof due to Weiss for the fact that topologically prime actions of sofic groups have non-positive topological sofic entropy.