Hui Xu

activity

20022026

most citedOn the "Mandelbrot set" for a pair of linear maps and complex Bernoulli convolutions

23 citations · 27 across the 23 of their papers we have counts for

collaborators

23 papers

math.DS2026

Cayley-tree pseudo-orbit tracing: period subgroups and relative geometry

Hui Xu

We introduce Cayley-tree POTP, obtained by imposing the pseudo-orbit equations of a finitely generated group action only along a spanning tree of a Cayley graph. For zero-dimension…

math.DS2024

Linearizations of periodic point free distal homeomorphisms on the annulus

Enhui Shi, Hui Xu, Ziqi Yu

Let $A$ be an annulus in the plane $R^{2}$ and $g : A \to A$ be a boundary components preserving homeomorphism which is distal and has no peri…

math.DS2024

The structure of periodic point free distal homeomorphisms on the annulus

Enhui Shi, Hui Xu, Ziqi YU

Let $A$ be an annulus in the plane $R^{2}$ and $g : A \to A$ be a boundary components preserving homeomorphism which is distal and has no periodic points. Then there is…

math.DS2024

Erdős' problem and $(n, \frac{1}{3})$ -separated sets

Enhui Shi, Hui Xu

Inspired by the Erdős' problem in Ramsey theory, we propose a dynamical version of the problem and answer it positively for circle maps.

math.DS2023

Groups acting distally and minimally on $S^{2}$ and $RP^{2}$

Enhui Shi, Hui Xu

Let $X$ be the $2$ -sphere $S^{2}$ or the real projective plane $RP^{2}$ . We show that if $Γ$ is a finitely generated group acting minimally and distally on $X$ , then…

math.DS2022

Disjointness with all minimal systems under group actions

Hui Xu, Xiangdong Ye

Let $G$ be a countable discrete group. We give a necessary and sufficient condition for a transitive $G$ -system to be disjoint with all minimal $G$ -systems, which implies that if a…

math.DS2022

The structures of higher rank lattice actions on dendrites

Enhui Shi, Hui Xu

Let $Γ$ be a higher rank lattice acting on a nondegenerate dendrite $X$ with no infinite order points. We show that there exists a nondegenerate subdendrite $Y$ which is $Γ$ -invari…

math.DS2022

Rigidity for higher rank lattice actions on dendrites

Enhui Shi, Hui Xu

We study the rigidity in the sense of Zimmer for higher rank lattice actions on dendrites and show that: (1) if $Γ$ is a higher rank lattice and $X$ is a nondegenerate dendrite wit…

math.DS2022

The nonexistence of expansive polycyclic group actions on the circle $S^{1}$

Enhui Shi, Suhua Wang, Zhiwen Xie +1

We show that the circle $S^{1}$ admits no expansive polycyclic group actions.

math.DS2022

On structure theorems and non-saturated examples

Qinqi Wu, Hui Xu, Xiangdong Ye

For any minimal system $(X, T)$ and $d \geq 1$ there is an associated minimal system $(N_{d} (X), G_{d} (T))$ , where $G_{d} (T)$ is the group generated by $T\times\c…

math.DS2022

The structure of pointwise recurrent expansive homeomorphisms

Enhui Shi, Hui Xu, Ziqi Yu

Let $X$ be a compact metric space and let $f : X \to X$ be a homeomorphism on $X$ . We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X…

math.DS2021★ 1 cited

The non-coexistence of distality and expansivity for group actions on infinite compacta

Bingbing Liang, Enhui Shi, Zhiwen Xie +1

Let $X$ be a compact metric space and $G$ a finitely generated group. Suppose $ϕ : G \to Homeo (X)$ is a continuous action. We show that if $ϕ$ is both distal and expansi…

math.DS2021

An alternative for minimal group actions on totally regular curves

Enhui Shi, Hui Xu, Xiangdong Ye

Let $G$ be a countable group and $X$ be a totally regular curve. Suppose that $ϕ : G \to Homeo (X)$ is a minimal action. Then we show an alternative: either the action is…

math.DS2021★ 1 cited

The nonexistence of expansive actions on Suslinian continua by groups of subexponential growth

Bingbing Liang, Enhui Shi, Zhiwen Xie +1

We show that if $G$ is a finitely generated group of subexponential growth and $X$ is a Suslinian continuum, then any action of $G$ on $X$ cannot be expansive.

math.DS2021

A dynamical argument for a Ramsey property

Enhui Shi, Hui Xu

We show by a dynamical argument that there is a positive integer valued function $q$ defined on positive integer set $N$ such that $q ([lo g n] + 1)$ is a super-polynomial wit…

math.DS2021★ 1 cited

Sensitive group actions on regular curves of almost $\leq n$ order

Suhua Wang, Enhui Shi, Hui Xu +1

Let $X$ be a regular curve and $n$ be a positive integer such that for every nonempty open set $U \subset X$ , there is a nonempty connected open set $V \subset U$ with the cardinalit…

math.DS2019

Invariant Radon measures and minimal sets for subgroups of $Homeo_{+} (R)$

Hui Xu, Enhui Shi, Yiruo Wang

Let $G$ be a subgroup of $Homeo_{+} (R)$ without crossed elements. We show the equivalence among three items: (1) existence of $G$ -invariant Radon measures on $\mathbb…

math.DS2019

Strongly Independent Matrices and Rigidity of $\times A$ -Invariant Measures on $n$ -Torus

Huichi Huang, Hanfeng Li, Enhui Shi +1

We introduce the concept of strongly independent matrices over any field, and prove the existence of such matrices for certain fields and the non-existence for algebraically closed…

math.DS2019

Commuting circle diffeomorphisms with their derivatives having mixed moduli of continuity

Hui Xu, Enhui Shi

Let $d \geq 2$ be an integer and let $ω_{1}, \dots, ω_{d}$ be moduli of continuity in a specified class which contains the moduli of Hölder continuity. Let $f_{k}$ , $k \in {1, \dots, d}$ ,…

math.DS2018★ 1 cited

Topological conjugation classes of tightly transitive subgroups of $Homeo_{+} (S^{1})$

Enhui Shi, Hui Xu

Let $Homeo_{+} (S^{1})$ denote the group of orientation preserving homeomorphisms of the circle $S^{1}$ . A subgroup $G$ of $Homeo_{+} (S^{1})$ is t…

math.CO2018

Monochromatic Regular Polygons in finitely colored $Z_{2} * Z_{2} * Z_{2}$

Hui Xu, Enhui Shi

We show that for any finite coloring of the group $Z_{2} * Z_{2} * Z_{2}$ and for any positive integer $k$ , there always exists a monochromatic regular $k$ -gon i…

math.DS2018

Strongly Independent Matrices and Applications on the Rigidity of $A$ -Invariant Measures on $n$ -Torus

Huichi Huang, Enhui Shi, Hui Xu

We introduce the notion of strongly independent matrices and show the existence of strongly independent matrices in $G L (n, Z)$ over $Z^{n} ∖ {0}$ when $2 n + 1$ …

math.DS2002★ 23 cited

On the "Mandelbrot set" for a pair of linear maps and complex Bernoulli convolutions

Boris Solomyak, Hui Xu

We consider the "Mandelbrot set" $M$ for pairs of complex linear maps, introduced by Barnsley and Harrington in 1985 and studied by Bousch, Bandt and others. It is defined as the s…

Cayley-tree pseudo-orbit tracing: period subgroups and relative geometry

Linearizations of periodic point free distal homeomorphisms on the annulus

The structure of periodic point free distal homeomorphisms on the annulus

Erdős' problem and (n,31​)-separated sets

Groups acting distally and minimally on S2 and RP2

Disjointness with all minimal systems under group actions

The structures of higher rank lattice actions on dendrites

Rigidity for higher rank lattice actions on dendrites

The nonexistence of expansive polycyclic group actions on the circle S1

On structure theorems and non-saturated examples

The structure of pointwise recurrent expansive homeomorphisms

The non-coexistence of distality and expansivity for group actions on infinite compacta

An alternative for minimal group actions on totally regular curves

The nonexistence of expansive actions on Suslinian continua by groups of subexponential growth

A dynamical argument for a Ramsey property

Sensitive group actions on regular curves of almost ≤n order

Invariant Radon measures and minimal sets for subgroups of Homeo+​(R)

Strongly Independent Matrices and Rigidity of ×A-Invariant Measures on n-Torus

Commuting circle diffeomorphisms with their derivatives having mixed moduli of continuity

Topological conjugation classes of tightly transitive subgroups of Homeo+​(S1)

Monochromatic Regular Polygons in finitely colored Z2​∗Z2​∗Z2​

Strongly Independent Matrices and Applications on the Rigidity of A-Invariant Measures on n-Torus

On the "Mandelbrot set" for a pair of linear maps and complex Bernoulli convolutions

Erdős' problem and $(n, \frac{1}{3})$ -separated sets

Groups acting distally and minimally on $S^{2}$ and $RP^{2}$

The nonexistence of expansive polycyclic group actions on the circle $S^{1}$

Sensitive group actions on regular curves of almost $\leq n$ order

Invariant Radon measures and minimal sets for subgroups of $Homeo_{+} (R)$

Strongly Independent Matrices and Rigidity of $\times A$ -Invariant Measures on $n$ -Torus

Topological conjugation classes of tightly transitive subgroups of $Homeo_{+} (S^{1})$

Monochromatic Regular Polygons in finitely colored $Z_{2} * Z_{2} * Z_{2}$

Strongly Independent Matrices and Applications on the Rigidity of $A$ -Invariant Measures on $n$ -Torus