某些算子类的 $\mathbb R$- 与 $\mathbb C$- 超循环性

加权复合算子在全纯函数空间上的动力学刚性

Dynamical rigidity for weighted composition operators on holomorphic function spaces

本文研究了加权复合算子在准巴纳赫全纯函数空间上的动力学刚性，通过诱导作用于周期轨道上的 jets，揭示了符号的局部全纯动力学限制，并在不同维度下证明了多项式自同构的加权刚性。

Topological conjugation classes of tightly transitive subgroups of $\text{Homeo}_{+}(\mathbb{S}^1)$

Let $\text{Homeo}_{+}(\mathbb{S}^1)$ denote the group of orientation preserving homeomorphisms of the circle $\mathbb{S}^1$. A subgroup $G$ of $\text{Homeo}_{+}(\mathbb{S}^1)$ is tightly transitive if it is topologically transitive and no subgroup $H$ of $G$ with $[G: H]=\infty$ has this property; is almost minimal if it has at most countably many nontransitive points. In the paper, we determine all the topological conjugation classes of tightly transitive and almost minimal subgroups of $\text{Homeo}_{+}(\mathbb{S}^1)$ which are isomorphic to $\mathbb{Z}^n$ for any integer $n\geq 2$.

On chain recurrence classes of endomorphisms of $\mathbb P^k$

We prove that the minimal chain recurrence classes of a holomorphic endomorphism of $\mathbb P^k$ have finitely many connected components. We also obtain results on arbitrary classes. These strong constraints on the topological dynamics in the phase space are all deduced from the associated action on a space of currents.

关于$\mathbb C$中的两类稠密2-生成子群

On two classes of dense 2-generator subgroups in $\mathbb C$

考虑$\mathbb C$中稠密的2-生成元乘法子群，证明了对于每个点$z\in \mathbb C$，每个生成元在点$z$处的幂的自变量的极限值集要么是有限的，要么是$[-π,π]$

有限型$\mathbb{Z}^d$子移位的增长型不变量与实数算术类

Growth-type invariants for $\mathbb{Z}^d$ subshifts of finite type and classes arithmetical of real numbers

本文讨论了与容许有限构型数目增长率有关的有限型多维移位（SFT）的一些数值不变量。扩展一个未发表的例子Tsirelson，我们表明，增长复杂性的形式$\exp(n^α)$是可能的非整数$α$的。在卡瓦略的术语中，这样的子移位具有熵维数$α$。根据Weihrauch和Zheng的实数的算术类确定了可能的$α$类。

Existence of robust non-uniformly hyperbolic endomorphism in homotopy classes

We extend the results of arXiv:2206.08295v2 by showing that any homothety in $\mathbb T^2$ is homotopic to a non-uniformly hyperbolic ergodic area preserving map, provided that its degree is at least $5^2$. We also address other small topological degree cases not considered in the previous article. This proves the existence of a $\mathcal C^1$ open set of non-uniformly hyperbolic systems, that intersects essentially every homotopy classes in $\mathbb T^2$, where the Lyapunov exponents vary continuously.