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pro vyhledávání: '"Xiao, Rongzhong"'
The paper gives some multi-dimensional extensions of Hindman's finite sum theorem. In particular, by the method of this paper, we prove that for any finite coloring of $\mathbb N$, there are $a,b\in \mathbb N$ such that there exist (infinitely many)
Externí odkaz:
http://arxiv.org/abs/2408.11661
Autor:
Lian, Zhengxing, Xiao, Rongzhong
In the paper, we searh for monochromatic infinite additive structures involving polynomials on $\mathbb{N}$. Ultimately, we can prove that for any $r\in \mathbb{N}$, any distinct natural numbers $a,b$ and any $2$-coloring of $\mathbb{N}$, there exist
Externí odkaz:
http://arxiv.org/abs/2404.05226
In this paper, we study the pointwise convergence of some continuous-time polynomial ergodic averages. Our method is based on the topological models of measurable flows. One of main results of the paper is as follow. Let $(X,\mathcal{X},\mu, (T^{t})_
Externí odkaz:
http://arxiv.org/abs/2310.16780
Autor:
Xiao, Rongzhong
In this paper, we extend the generalized Wiener-Wintner Theorem built by Host and Kra to the multilinear case under the hypothesis of pointwise convergence of multilinear ergodic averages. In particular, we have the following result: Let $(X,\mathcal
Externí odkaz:
http://arxiv.org/abs/2303.02676
Autor:
Xiao, Rongzhong
Let $k,a\in \mathbb{N}$ and let $p_1,\cdots,p_k\in \mathbb{Q}[n]$ with zero constant term. We show that for any finite coloring of $\mathbb{Q}$, there are non-zero $x,y\in \mathbb{Q}$ such that there exists a color which contains a set of the form $$
Externí odkaz:
http://arxiv.org/abs/2212.09244
Autor:
Xiao, Rongzhong
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 c
Externí odkaz:
http://arxiv.org/abs/2206.02197
Let $G$ be an infinite countable discrete amenable group. For any $G$-action on a compact metric space $X$, it is proved that for any sequence $(G_n)_{n\ge 1}$ consisting of non-empty finite subsets of $G$ with $\lim_{n\to \infty}|G_n|=\infty$, Pinsk
Externí odkaz:
http://arxiv.org/abs/2202.12503
Autor:
Xiao, Rongzhong
Publikováno v:
In Journal of Differential Equations 15 April 2024 388:403-420
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