Bohr chaoticity of topological dynamical systems

主代数作用的Bohr混沌性与Riesz乘积测度

Bohr chaoticity of principal algebraic actions and Riesz product measures

该研究提出拓扑共轭不变的Bohr混沌性概念（强于正熵），证明正熵主代数$\u2124$作用均为Bohr混沌，且$d\ge2$时正熵主代数$\u2124^d$作用在可和同宿点存在条件下也满足该性质。

Bohr混沌性、半马尔可夫游动与全熵丰富性

Bohr chaoticity, semi-horseshoes and full-entropy abundance

本文证明具有半马尔可夫游动的动力系统具有Bohr混沌性，并展示了与非平凡权重相关联的点集具有正拓扑熵，进一步在经典代数和光滑设置及拓扑动力学的C^0-泛泛设置中应用。

Dynamics of Bohr almost periodic motions of topological abelian semigroups

We study the topological and ergodic dynamics of Bohr almost periodic motions of a topological abelian semigroup acting continuously on a compact metric space.

Definable topological dynamics

For a group $G$ definable in a first order structure $M$ we develop basic topological dynamics in the category of definable $G$-flows. In particular, we give a description of the universal definable $G$-ambit and of the semigroup operation on it. We find a natural epimorphism from the Ellis group of this flow to the definable Bohr compactification of $G$, that is to the quotient $G^*/{G^*}^{00}_M$ (where $G^*$ is the interpretation of $G$ in a monster model). More generally, we obtain these results locally, i.e. in the category of $Δ$-definable $G$-flows for any fixed set $Δ$ of formulas of an…

Special cases and equivalent forms of Katznelson's problem on recurrence

We make three observations regarding a question popularized by Katznelson: is every subset of $\mathbb Z$ which is a set of Bohr recurrence is also a set of topological recurrence? (i) If $G$ is a countable abelian group and $E\subset G$ is an $I_0$ set, then every subset of $E-E$ which is a set of Bohr recurrence is also a set of topological recurrence. In particular every subset of $\{2^n-2^m : n,m\in \mathbb N\}$ which is a set of Bohr recurrence is a set of topological recurrence. (ii) Let $\mathbb Z^ω$ be the direct sum of countably many copies of $\mathbb Z$ with standard basis $E$. If e…

拓扑动力系统的Wiener--Wintner点

Wiener--Wintner points for topological dynamical systems

该文研究局部紧阿贝尔群上的动力系统，将Wiener-Wintner型平均收敛性与系统特征值关联，提出Wiener--Wintner点概念并证明其遍历情形下满测度，还明确了其在非周期序模型中与衍射理论的对应关系。