Residuality of Dynamical Morphisms for Amenable Group Actions

2024/06/18 by Dawid Huczek, Huczek, Dawid, Sebastian Kopacz +3
Computer Science · Mathematics · #37A35 #37B10 #37C85 #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Primary 37A15 #Secondary 28D15 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2406.13004

openalex publication_date 2024/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the classical Baire category approach, used in proving the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein, applying a similar reasoning to the case of actions of countably infinite amenable groups. In principle we follow the lines of the paper by Burton, Keane and Serafin (\citeBKS), showing that measures defining homomorphisms or isomorphisms form residual subsets in suitably chosen spaces of joinings.

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