Continua having distal minimal actions by amenable groups

可测远端群作用的不相交性及其应用

Disjointness for measurably distal group actions and applications

本研究将Berg拟不相交性推广至可数群作用，证明可测远端系统与保测系统拟不相交，给出易检验的不相交充要条件，还得到带远端权重的可数顺从群Wiener--Wintner型定理及在遍历平均、多重回复中的应用。

Periodic points for amenable group actions on uniquely arcwise connected continua

We show that if $G$ is a countable amenable group acting on a uniquely arcwise connected continuum $X$, then $G$ has either a fixed point or a 2-periodic point in $X$.

关于拓扑全群的顺从性与LEF性质

On Amenability and LEF-ness for topological full groups

本文证明了拓扑自由远端作用的拓扑全群顺从性等价于底群顺从，并推广了LEF性质到剩余有限作用，进而证明自由群上某些Toeplitz子位移的拓扑全群是LEF且sofic。

连续统的同胚群的泛最小流

Universal minimal flows of homeomorphism groups of continua

通过定义射影Fraïssé范畴的近似Ramsey性质，证明了该性质与群极端可安性等价，并应用于伪螺线管同胚群得到非可度量化泛最小流。

The structure of tame minimal dynamical systems for general groups

We use the structure theory of minimal dynamical systems to show that, for a general group $Γ$, a tame, metric, minimal dynamical system $(X, Γ)$ has the following structure: \begin{equation*} \xymatrix {& \tilde{X} \ar[dd]_π\ar[dl]_η& X^* \ar[l]_-{θ^*} \ar[d]^ι \ar@/^2pc/@{>}^{π^*}[dd]\\ X & & Z \ar[d]^σ\\ & Y & Y^* \ar[l]^θ} \end{equation*} Here (i) $\tilde{X}$ is a metric minimal and tame system (ii) $η$ is a strongly proximal extension, (iii) $Y$ is a strongly proximal system, (iv) $π$ is a point distal and RIM extension with unique section, (v) $θ$, $θ^*$ and $ι$ are almost one-to-one ext…