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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2510.17267 |
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| _version_ | 1866908602820722688 |
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| author | Ouyang, Kangbo Wu, Qinqi |
| author_facet | Ouyang, Kangbo Wu, Qinqi |
| contents | A topological dynamical system $(X,T)$ is called CF-Nil($k$) if it is strictly ergodic and the maximal measurable and maximal topological $k$-step pro-nilfactors coincide as measure preserving systems. Through constructing specific ``CF-Nil'' models, we prove that for any ergodic system $(X,\mathcal{X},μ,T)$, any nilsequence $\{ψ(m,n)\}_{m,n\in\mathbb{Z}}$ and any $f_1,\dots,f_d\in L^{\infty}(μ)$, the averages
\begin{equation*}
\dfrac{1}{N^{2}} \sum_{m,n=0}^{N-1} ψ(m,n)\prod_{j=1}^{d}f_{j}(T^{m+jn}x)
\end{equation*}
converge pointwise as $N$ goes to infinity. Moreover, we show the $L^2$-convergence of a certain two-dimensional averages for non-commuting transformations without zero entropy condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | CF-Nil systems and convergence of two-dimensional ergodic averages Ouyang, Kangbo Wu, Qinqi Dynamical Systems A topological dynamical system $(X,T)$ is called CF-Nil($k$) if it is strictly ergodic and the maximal measurable and maximal topological $k$-step pro-nilfactors coincide as measure preserving systems. Through constructing specific ``CF-Nil'' models, we prove that for any ergodic system $(X,\mathcal{X},μ,T)$, any nilsequence $\{ψ(m,n)\}_{m,n\in\mathbb{Z}}$ and any $f_1,\dots,f_d\in L^{\infty}(μ)$, the averages \begin{equation*} \dfrac{1}{N^{2}} \sum_{m,n=0}^{N-1} ψ(m,n)\prod_{j=1}^{d}f_{j}(T^{m+jn}x) \end{equation*} converge pointwise as $N$ goes to infinity. Moreover, we show the $L^2$-convergence of a certain two-dimensional averages for non-commuting transformations without zero entropy condition. |
| title | CF-Nil systems and convergence of two-dimensional ergodic averages |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.17267 |