Polynomial ergodic averages of measure-preserving systems acted by $\mathbb{Z}^{d}$
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917631973392384 |
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| author | Xiao, Rongzhong |
| author_facet | Xiao, Rongzhong |
| contents | 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 $\mathbb{Z}^{d}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_02197 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Polynomial ergodic averages of measure-preserving systems acted by $\mathbb{Z}^{d}$ Xiao, Rongzhong Dynamical Systems 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 $\mathbb{Z}^{d}$. |
| title | Polynomial ergodic averages of measure-preserving systems acted by $\mathbb{Z}^{d}$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2206.02197 |