Expansivity and unique shadowing

Bi-Asymptotic $c$-Expansivity

In this paper, we define bi-asymptotically $c$-expansive maps on metric spaces and study its relationship with other variants of expansivity such as bi-asymptotically expansive maps and $N$-expansive maps. We also provide an example to establish that expansive homeomorphisms need not be bi-asymptotically expansive. Finally we prove a spectral decomposition theorem for bi-asymptotically $c$-expansive continuous surjective maps with the shadowing property on compact metric spaces.

具有伪轨跟踪性质的可数膨胀与熵膨胀同胚

Countably and entropy expansive homeomorphisms with the shadowing property

本文研究具有伪轨跟踪性质的可数膨胀与熵膨胀同胚，证明传递可数膨胀同胚在传递点集上膨胀，并证明在曲面情形下可数膨胀和熵cw-膨胀均等价于拓扑共轭于阿诺索夫微分同胚。

局部凸空间上算子的广义双曲性、稳定性与扩张性

Generalized Hyperbolicity, Stability and Expansivity for Operators on Locally Convex Spaces

本文研究局部凸空间上算子的广义双曲性、拓扑稳定性与拓扑扩张性，建立其与有限跟踪、严格周期跟踪、混沌及传递性之间的关系，并刻画加权移位情形。

集值映射的周期跟踪性

Periodic Shadowing for Set-Valued Maps

研究集值动力系统的周期跟踪性质，证明在紧度量空间上正膨胀集值映射的跟踪性蕴含周期跟踪性，且链传递映射的周期跟踪性蕴含跟踪性和拓扑传递性。

Pointwise dynamics under Orbital Convergence

We obtain sufficient conditions under which the limit of a sequence of functions exhibits a particular dynamical behaviour at a point like expansivity, shadowing, mixing, sensitivity and transitivity. We provide examples to show that the set of all expansive, positively expansive and sensitive points are neither open nor closed in general. We also observe that the set of all transitive and mixing points are closed but not open in general. We give examples to show that properties like expansivity, sensitivity, shadowing, transitivity and mixing at a point need not be preserved under uniform con…

具有跟踪性的随机 \(cw -\) 扩张系统的拓扑稳定性

Topological Stability of Random $cw$-Expansive Systems with Shadowing

研究随机动力系统的拓扑稳定性，通过随机连续扩张性和跟踪性概念扩展经典结果，证明相关系统随机拓扑稳定，还建立性质共轭下拓扑不变性并分析拓扑传递性与周期跟踪性的关系。

Shadowing maps（跟踪映射）

Shadowing maps

本文针对紧度量空间同胚的跟踪性质，提出跟踪映射的理论与层级体系，结合Bowen的经典方法从双曲括号构造自调谐跟踪映射，丰富了跟踪性相关研究。

Shadowing, internal chain transitivity and $α$-limit sets

Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $α_f$, $ω_f$ and $ICT_f$ denote the set of $α$-limit sets, $ω$-limit sets and nonempty closed internally chain transitive sets respectively. We show that if the map $f$ has shadowing then every element of $ICT_f$ can be approximated (to any prescribed accuracy) by both the $α$-limit set and the $ω$-limit set of a full-trajectory. Furthermore, if $f$ is additionally c-expansive then every element of $ICT_f$ is equal to both the $α$-limit set and the $ω$-limit set of a full-trajectory. In particular this means that …

Expansivity properties and rigidity for non-recurrent exponential maps

We show that an exponential map $f_c(z)=e^z+c$ whose singular value $c$ is combinatorially non-recurrent and non-escaping is uniquely determined by its combinatorics, i.e. the pattern in which its dynamic rays land together. We do this by constructing puzzles and parapuzzles in the exponential family. We also prove a theorem about hyperbolicity of the postsingular set in the case that the singular value is non-recurrent. Finally, we show that boundedness of the postsingular set implies combinatorial non-recurrence if $c$ is in the Julia set.

Schwartz空间上复合算子的线性动力学

Linear dynamics of composition operators on Schwartz spaces

该研究分析Schwartz空间上复合算子的线性动力学，证明可逆复合算子非广义双曲、符号有不动点时算子无正阴影性质，给出符号使算子正拓扑膨胀的条件，刻画仿射符号并明确奇偶次多项式符号的膨胀性差异。

乘积阿诺索夫微分同胚与双侧极限跟踪性质

Product Anosov diffeomorphisms and the two-sided limit shadowing property

本文用双侧极限跟踪性质刻画乘积阿诺索夫微分同胚，证明其等价于万有覆盖上提升的唯一双侧极限跟踪性质，并通过巴拿赫空间中映射的不动点关联跟踪轨道。

$H^{2}(\mathbb{C}_{+})$ 上复合算子的动力学性质

Dynamical properties for composition operators on $H^{2}(\mathbb{C}_{+})$

本文基于线性动力学中扩张性、Li-Yorke混沌与跟踪的刻画，研究了右半平面仿射自映射在 Hardy-Hilbert 空间上诱导的复合算子的这三种动力学性质。