集值映射的规范性质及其逆极限

Topological entropy of diagonal maps on inverse limit spaces

We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal component is the same map $g\colon I\to I$ which strongly commutes with $f$ (i.e. $f^{-1}\circ g=g\circ f^{-1}$), we show that the entropy equals $\max\{\textrm{Ent}(f),\textrm{Ent}(g)\}$. As a side product, we develop some techniques for computing topological entropy of set-valued maps.

Periodicity and Indecomposability in Generalized Inverse Limits

In this paper, we consider inverse limits of [0,1] using upper semicontinuous set-valued bonding functions with the intermediate value property. Expanding on classical results by Barge and Martin, we explore the relationship between periodicity in the bonding function and the topology of the corresponding inverse limit. In particular, for an inverse limit of a single upper semicontinuous bonding map with the intermediate value property, we provide sufficient conditions for the existence of a periodic cycle with period not a power of two in the bonding function to imply the existence of an inde…

即使是弱规格性质也蕴含遍历测度的稠密性

Even the vague specification property implies density of ergodic measures

本文证明了满射拓扑动力系统若具有弱规格性质，则其遍历测度在不变测度空间中稠密，核心方法是通过 $δ$-链子系统逼近自然扩展，并利用链混合与周期规格性质完成极限过渡。

向量外微分系统的对称性与二阶Ostrohrads'Kyj力学的反问题

Symmetries of vector exterior differential systems and the inverse problem in second-order Ostrohrads'kyj mechanics

变分问题的对称性被认为是向量丛值外微分系统的对称性。然后将这种方法应用于半经典自旋粒子运动的三阶常变分方程。