Joint ergodicity along generalized linear functions

2014/09/25 by Vitaly Bergelson, Bergelson, Vitaly, A. Leibman +5
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #advanced mathematical theories #math.DS

paper · pdf · doi:10.48550/arxiv.1409.7151

arxiv created 2014/09/25 · openalex publication_date 2014/09/25 · arxiv updated 2014/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A criterion of joint ergodicity of several sequences of transformations of a probability measure space X of the form T_i^ϕ_i(n) is given for the case where T_i are commuting measure preserving transformations of X and ϕ_i are integer valued generalized linear functions, that is, the functions formed from conventional linear functions by an iterated use of addition, multiplication by constants, and the greatest integer function. We also establish a similar criterion for joint ergodicity of families of transformations depending of a continuous parameter, as well as a condition of joint ergodicity of sequences T_i^ϕ_i(n) along primes.

Citations

• Multiple recurrence and convergence for Hardy sequences of polynomial growth

Related

• Joint ergodicity of sequences
• Joint ergodicity for commuting transformations and applications to polynomial sequences
• Joint ergodicity for functions of polynomial growth
• Decomposition of multicorrelation sequences and joint ergodicity
• Resolving the joint ergodicity problem for Hardy sequences