Hui Xu

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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.DS2025

Structure theorems of commuting transformations and minimal $R$ -flows

Song Shao, Hui Xu

In this paper, we develop several structure theorems concerning commuting transformations and minimal $R$ -flows. Specifically, we show that if $(X, S)$ , $(X, T)$ are minimal…

math.DS2025

On systems disjoint from all minimal systems

Wen Huang, Song Shao, Hui Xu +1

Recently, Górska, Lemańczyk, and de la Rue characterized the class of automorphisms disjoint from all ergodic automorphisms. Inspired by their work, we provide several characteriza…

On subsets of integers having dense orbits

Structure theorems of commuting transformations and minimal R-flows

On systems disjoint from all minimal systems

Structure theorems of commuting transformations and minimal $R$ -flows