Polynomial ergodic averages of measure-preserving systems acted by $\mathbb{Z}^{d}$

Rongzhong Xiao

doi:10.1016/j.jde.2024.01.020

Polynomial ergodic averages of measure-preserving systems acted by $\mathbb{Z}^{d}$

Dynamical Systems 2024-04-09 v2

Authors: Rongzhong Xiao

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

In this paper, we reduce pointwise convergence of polynomial ergodic averages of general measure-preserving system acted by $\mathbb{Z}^{d}$ to the case of measure-preserving system acted by $\mathbb{Z}^{d}$ with zero entropy. As an application, we can build pointwise convergence of polynomial ergodic averages for $K$ -system acted by $\mathbb{Z}^{d}$ .

Keywords

polynomial ergodic averages measure-preserving systems pointwise convergence zero entropy k-systems zd action

Cite

@article{arxiv.2206.02197,
  title  = {Polynomial ergodic averages of measure-preserving systems acted by $\mathbb{Z}^{d}$},
  author = {Rongzhong Xiao},
  journal= {arXiv preprint arXiv:2206.02197},
  year   = {2024}
}

Related papers

View all related →