Enhui Shi

activity

20142025

most citedPeriodic points for amenable group actions on uniquely arcwise connected continua

2 citations · 11 across the 33 of their papers we have counts for

collaborators

35 papers

math.DS2025

A note on the bounded orbit conjecture

Enhui Shi, Ziqi Yu

If $f : R^{2} \to R^{2}$ is an orientation reversing fixed point free homeomorphism on the plane $R^{2}$ with no unbounded orbit, then $f$ has infinitely…

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

$(ω, α, n)$ -sensitivity and limit sets of zero entropy homeomorphisms on the square

Jiehua Mai, Enhui Shi, Kesong Yan +1

For a homeomorphism $f$ of a compact metric space $X$ and a positive integer $n \geq 2$ , we introduce the notion of $(ω, α, n)$ -sensitivity of $f$ , which describes such a kind of ch…

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

A new construction of counterexamples to the bounded orbit conjecture

Jiehua Mai, Enhui Shi, Kesong Yan +1

The bounded orbit conjecture says that every homeomorphism on the plane with each of its orbits being bounded must have a fixed point. Brouwer's translation theorem asserts that th…

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.DS2024

Can points of bounded orbits surround points of unbounded orbits ?

Jiehua Mai, Enhui Shi, Kesong Yan +1

We show a somewhat surprising result: if $E$ is a disk in the plane $R^{2}$ , then there is a homeomorphism $h : R^{2} \to R^{2}$ such that, for every $x\in\pa…

math.DS2024

Some extensions of the Brouwer fixed point theorem

Jiehua Mai, Enhui Shi, Kesong Yan +1

We study the existence of fixed points for continuous maps $f$ from an $n$ -ball $X$ in $R^{n}$ to $R^{n}$ with $n \geq 1$ . We show that $f$ has a fixed point if, for som…

math.DS2024

Quasi-intermediate value theorem and outflanking arc theorem for plane maps

Jiehua Mai, Enhui Shi, Kesong Yan +1

For a disk $D$ in the plane $R^{2}$ and a plane map $f$ , we give several conditions on the restriction of $f$ to the boundary $\partial D$ of $D$ which imply the existence of…

math.DS2023

Structures of $R (f) - P (f)$ for graph maps $f$

Jiehua Mai, Enhui Shi, Kesong Yan +1

Let $G$ be a graph and $f : G \to G$ be a continuous map. We establish a structure theorem which describes the structures of the set $R (f) - P (f)$ , where $R (f)$ and…

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

The structures of pointwise recurrent quasi-graph maps

Ziqi Yu, Suhua Wang, Enhui Shi

We show that a continuous map $f$ from a quasi-graph $G$ to itself is pointwise recurrent if and only if one of the following two statements holds: (1) $X$ is a simple closed curve…

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

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.DS2020★ 1 cited

Continua having distal minimal actions by amenable groups

Enhui Shi

Let $X$ be a non-degenerate connected compact metric space. If $X$ admits a distal minimal action by a finitely generated amenable group, then the first \vCech cohomology group $ {…

math.DS2020★ 2 cited

Distal higher rank lattice actions on surfaces

Enhui Shi

Let $Γ$ be a lattice in $SL (n, R)$ with $n \geq 3$ and $S$ be a closed surface. Then $Γ$ has no distal minimal action on $S$ .

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…

A note on the bounded orbit conjecture

Linearizations of periodic point free distal homeomorphisms on the annulus

(ω,α,n)-sensitivity and limit sets of zero entropy homeomorphisms on the square

The structure of periodic point free distal homeomorphisms on the annulus

A new construction of counterexamples to the bounded orbit conjecture

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

Can points of bounded orbits surround points of unbounded orbits ?

Some extensions of the Brouwer fixed point theorem

Quasi-intermediate value theorem and outflanking arc theorem for plane maps

Structures of R(f)−P(f)​ for graph maps f

Groups acting distally and minimally on S2 and RP2

The structures of pointwise recurrent quasi-graph maps

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

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

Continua having distal minimal actions by amenable groups

Distal higher rank lattice actions on surfaces

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

$(ω, α, n)$ -sensitivity and limit sets of zero entropy homeomorphisms on the square

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

Structures of $R (f) - P (f)$ for graph maps $f$

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 $Homeo_{+} (R)$