Jian Li

activity

20102026

most citedMean equicontinuity and mean sensitivity

115 citations · 746 across the 51 of their papers we have counts for

collaborators

53 papers

math.DS2026

Return Time Sets of Minimal Points for Countable Group Actions

Jian Li, Yini Yang

For a countably infinite discrete group $G$ , we study subsets of $G$ that contain a neighbourhood return-time set of a minimal point in a $G$ -flow $X$ . For $e \in F \subseteq G$ , we…

math.FA2026

Typical dynamical properties of operators on $ℓ_{p}$

Jian Li, Qijing Liao

We investigate the typical dynamical properties of hypercyclic operators in $L_{M} (X)$ , the set of all bounded linear operators on $X$ whose norms are at most $M$ , when $X=…

math.DS2026

The equivalence of precompactness, zero maximal pattern entropy and bounded mean complexity for finite partitions

Jian Li, Tao Yu, Xianliang Zhong

In this paper, we investigate several types of low complexity of finite partitions, including precompactness, zero maximal pattern entropy, bounded mean complexity and mean equicon…

math.DS2025

Weak disjointness of hypercyclic operators

Jian Li, Qijing Liao, Yonghang Ruan

We study the weak disjointness of hypercyclic operators to refine the classifications of hypercyclic operators. We establish an analogue of the Weiss-Akin-Glasner Theorem from topo…

math.FA2025

Mean Li-Yorke chaos for a sequence of operators on Banach spaces

Jian Li, Xinsheng Wang, Jianjie Zhao

In this paper, we obtain the dichotomy for mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space. The mea…

math.FA2025

Density properties of orbits for a hypercyclic operator on a Banach space

Jian Li, Xinsheng Wang, Jianjie Zhao

We study density properties of orbits for a hypercyclic operator $T$ on a separable Banach space $X$ , and show that exactly one of the following four cases holds: (1) every vector…

math.FA2025

Distributionally chaotic $C_{0}$ -semigroups on complex sectors

Zhen Jiang, Jian Li, Yini Yang

We explore distributional chaos for $C_{0}$ -semigroups of linear operators on Banach spaces whose index set is a sector in the complex plane. We establish the relationship between di…

math.DS2025★ 1 cited

Dense uniform Li-Yorke chaos for linear operators on a Banach space

Jian Li, Xinsheng Wang

This paper focuses on the dense uniform Li-Yorke chaos for linear operators on a Banach space. Some sufficient conditions and equivalent conditions are established under which the…

math.DS2025

A note on logarithmic mean equicontinuity

Dominik Kwietniak, Jian Li, Habibeh Pourmand

We study the set of harmonic limits of empirical measures in topological dynamical systems. We obtain a characterization of unique ergodicity based of logarithmic (harmonic) mean c…

math.FA2024

Trichotomy for the orbits of a hypercyclic operator on a Banach space

Jian Li

We obtain a trichotomy for the orbits of a hypercyclic operator $T$ on a separable Banach space $X$ : (1) every vector is mean asymptotic to zero; (2) generic vectors are absolutely…

math.DS2024

Return time sets and product recurrence

Jian Li, Xianjuan Liang, Yini Yang

Let $G$ be a countable infinite discrete group. We show that a subset $F$ of $G$ contains a return time set of some piecewise syndetic recurrent point $x$ in a compact Hausdorff sp…

math.DS2023★ 2 cited

The mean orbital pseudo-metric and the space of invariant measures

Jian Li, Yuanfen Xiao

We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures. We give equivalent conditions for when…

math.DS2023★ 1 cited

Characterizations of distality via weak equicontinuity

Jian Li, Yini Yang

For an infinite discrete group $G$ acting on a compact metric space $X$ , we introduce several weak versions of equicontinuity along subsets of $G$ and show that if a minimal system…

math.DS2023★ 14 cited

On the properties of the mean orbital pseudo-metric

Fangzhou Cai, Dominik Kwietniak, Jian Li +1

Given a topological dynamical system $(X, T)$ , we study properties of the mean orbital pseudo-metric $E ˉ$ defined by \[ \bar E(x,y)= \limsup_{n\to\infty } \min_{σ\in S_n}\frac{1…

math.DS2022★ 5 cited

Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces

Zhen Jiang, Jian Li

Using some techniques from topological dynamics, we give a uniform treatment of Li-Yorke chaos, mean Li-Yorke chaos and distributional chaos for continuous endomorphisms of complet…

math.DS2022★ 1 cited

A dynamical approach to nonhomogeneous spectra

Jian Li, XianJuan Liang

Let $α > 0$ and $0 < γ < 1$ . Define $g_{α, γ} : N \to N_{0}$ by $g_{α, γ} (n) = ⌊ n α + γ ⌋$ , where $⌊ x ⌋$ is the largest integer less than or equal to…

math.DS2022★ 1 cited

Broken family sensitivity in transitive systems

Jian Li, Yini Yang

Let $(X, T)$ be a topological dynamical system, $n \geq 2$ and $F$ be a Furstenberg family of subsets of $Z_{+}$ . $(X, T)$ is called broken $F$ - $n$ -sensitiv…

math.DS2021★ 2 cited

Graph maps with zero topological entropy and sequence entropy pairs

Jian Li, Xianjuan Liang, Piotr Oprocha

We show that graph map with zero topological entropy is Li-Yorke chaotic if and only if it has an NS-pair (a pair of non-separable points containing in a same solenoidal $ω$ -limit…

math.DS2021★ 6 cited

On $n$ -tuplewise IP-sensitivity and thick sensitivity

Jian Li, Yini Yang

Let $(X, T)$ be a topological dynamical system and $n \geq 2$ . We say that $(X, T)$ is $n$ -tuplewise IP-sensitive (resp. $n$ -tuplewise thickly sensitive) if there exists a constant $δ…

math.DS2020★ 3 cited

$Δ$ -weakly mixing subsets along a collection of sequences of integers

Jian Li, Kairan Liu

In this paper, we propose a mild condition, named Condition $(* *)$ , for collections of sequence of integers and show that for any measure preserving system the Pinsker $σ$ -algebra…

math.DS2020★ 11 cited

Stronger versions of sensitivity for minimal group actions

Jian Li, Yini Yang

We study several stronger versions of sensitivity for minimal group actions, including $n$ -sensitivity, thick $n$ -sensitivity and blockily thick $n$ -sensitivity, and characterize t…

math.DS2020★ 3 cited

The topological structure of function space of transitive maps

Zhaorong He, Jian Li, Zhongqiang Yang

Let $C (I)$ be the set of all continuous self-maps from $I = [0, 1]$ with the topology of uniformly convergence. A map $f \in C (I)$ is called a transitive ma…

math.DS2020★ 10 cited

Positive entropy implies chaos along any infinite sequence

Wen Huang, Jian Li, Xiangdong Ye

Let $G$ be an infinite countable discrete amenable group. For any $G$ -action on a compact metric space $(X, ρ)$ , it turns out that if the action has positive topological entropy, th…

math.DS2019★ 2 cited

Subspaces of interval maps related to the topological entropy

Xiaoxin Fan, Jian Li, Yini Yang +1

For $a \in [0, + \infty)$ , the function space $E_{\geq a}$ ( $E_{> a}$ ; $E_{\leq a}$ ; $E_{< a}$ ) of all continuous maps from $[0, 1]$ to itself whose topological entropies are larger than…

Return Time Sets of Minimal Points for Countable Group Actions

Typical dynamical properties of operators on ℓp​

The equivalence of precompactness, zero maximal pattern entropy and bounded mean complexity for finite partitions

Weak disjointness of hypercyclic operators

Mean Li-Yorke chaos for a sequence of operators on Banach spaces

Density properties of orbits for a hypercyclic operator on a Banach space

Distributionally chaotic C0​-semigroups on complex sectors

Dense uniform Li-Yorke chaos for linear operators on a Banach space

A note on logarithmic mean equicontinuity

Trichotomy for the orbits of a hypercyclic operator on a Banach space

Return time sets and product recurrence

The mean orbital pseudo-metric and the space of invariant measures

Characterizations of distality via weak equicontinuity

On the properties of the mean orbital pseudo-metric

Chaos for endomorphisms of completely metrizable groups and linear operators on Fréchet spaces

A dynamical approach to nonhomogeneous spectra

Broken family sensitivity in transitive systems

Graph maps with zero topological entropy and sequence entropy pairs

On n-tuplewise IP-sensitivity and thick sensitivity

Δ-weakly mixing subsets along a collection of sequences of integers

Stronger versions of sensitivity for minimal group actions

The topological structure of function space of transitive maps

Positive entropy implies chaos along any infinite sequence

Subspaces of interval maps related to the topological entropy

Typical dynamical properties of operators on $ℓ_{p}$

Distributionally chaotic $C_{0}$ -semigroups on complex sectors

On $n$ -tuplewise IP-sensitivity and thick sensitivity

$Δ$ -weakly mixing subsets along a collection of sequences of integers