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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.