Several remarks on Pascal automorphism and infinite ergodic theory

2015/12/11 by A. M. Vershik, Anatoly Vershik, Vershik, Anatoly
Computer Science · Mathematics · #28E99 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories #math.DS #msc:28E99

paper · pdf · doi:10.48550/arxiv.1512.03721

14 pp,Ref.16

arxiv created 2015/12/11 · openalex publication_date 2015/12/11 · arxiv updated 2015/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We interpret the Pascal-adic transformation as a generalized induced automorphism (over odometer) and formulate the σ-finite analog of odometer which is also known as "Hajian-Kakutani transformation" (former "Ohio state example"). We shortly suggest a sketch of the theory of random walks on the groups on the base of σ-finite ergodic theory.

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