Jiahao Qiu

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20212026

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6 papers · 1 filter

math.DS2026

Connectedness of polynomial diagonal orbit closures for minimal nilrotations and applications

Kangbo Ouyang, Jiahao Qiu, Xiangdong Ye

For a minimal nilrotation on a compact connected nilmanifold, we prove that the polynomial diagonal orbit closure associated with any finite family of polynomials with integer coef…

math.DS2026

Zero-Threshold Discrepancies for Multiple Correlation Sequences

Kangbo Ouyang, Jiahao Qiu, Xiangdong Ye

We study the zero-threshold lifting problem for polynomial multiple correlation sequences with respect to the measure-theoretic pro-nilfactor. The structure theory for polynomial m…

math.DS2026

On subsets of integers having dense orbits

Zhuowen Guo, Jiahao Qiu, Hui Xu +1

Let $A \subset N$ . We say $A$ is an $R$ -sequence for a given minimal system $(Y, S)$ if there is $y \in Y$ such that ${S^{n} y : n \in A}$ is dense in $Y$ . Richter asked if $A$ i…

math.DS2024

Veech's theorem of higher order

Jiahao Qiu, Xiangdong Ye

For an abelian group $G$ , $g = (g_{1}, \dots, g_{d}) \in G^{d}$ and $ε = (ε (1), \dots, ε (d)) \in {0, 1}^{d}$ , let $g \cdot ε = \prod_{i = 1}^{d} g_{i}^{ε (i)}$ . In this paper, it is shown that…

math.DS2023

Saturated theorem along cubes for a measure and applications

Jiahao Qiu, Jiaqi Yu

We show that for a minimal system $(X, T)$ , the set of saturated points along cubes with respect to its maximal $\infty$ -step pro-nilfactor $X_{\infty}$ has a full measure. As an appl…

math.DS2021

Independence and almost automorphy of high order

Jiahao Qiu

In this paper, it is shown that for a minimal system $(X, T)$ and $d, k \in N$ , if $(x, x_{i})$ is regionally proximal of order $d$ for $1 \leq i \leq k$ , then $(x,x_1,\ldots,x_k)…