Quasi-similarity, entropy and disjointness of ergodic systems

2023/03/16 by Valery V. Ryzhikov, Ryzhikov, Valery V., Jean‐Paul Thouvenot +1
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2303.09546

openalex publication_date 2023/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Answering Vershik's question we show that quasi-similarity does not conserve the entropy, proving quasi-similarity of all Bernoulli actions of a countable infinite group. We prove also the following generalization of Pinsker's theorem: the actions with zero Kirillov-Kushnirenko P-entropy and the actions with completely positive P-entropy are disjoint. Poisson suspensions are used as examples.

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