Ergodic Behaviour of Nonconventional Ergodic Averages for Commuting Transformations

Ergodic Behaviour of Nonconventional Ergodic Averages for Commuting Transformations

Year:    2019

Author:    Xia Pan, Zuohuan Zheng, Zhe Zhou

Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 4 : pp. 513–525

Abstract

Based on T. Tao's celebrated result on the norm convergence of multiple ergodic averages for commuting transformations, we find that there is a subsequence which converges almost everywhere. Meanwhile, we obtain the ergodic behaviour of diagonal measures, which indicates the time average equals the space average. According to the classification of transformations, we also give several different results. Additionally, on the torus $\mathbb{T}^d$ with special rotation, we prove the pointwise convergence in $\mathbb{T}^d$ , and get a result for ergodic behaviour.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.12150/jnma.2019.513

Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 4 : pp. 513–525

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Commuting transformation convergence almost everywhere ergodic behaviour time average space average.

Author Details

Xia Pan

Zuohuan Zheng

Zhe Zhou