关于封闭吸引器的拓扑特性
On topological properties of closed attractors
Wouter Jongeneel
arXiv
2025年11月13日
吸引者的概念在动力学系统理论中有各种定义。 在紧凑性假设下,其中一些定义是一致的,理论相当完整。 然而,没有紧凑,画面就变得模糊。 为了提高我们的理解,我们在这项工作中表征了一个封闭,不一定是紧凑的,在本地紧凑的度量空间上相对稳定的吸引器,相当于其吸引力域。 这能够进一步对相应的反馈稳定问题进行结构研究。
The notion of an attractor has various definitions in the theory of dynamical systems. Under compactness assumptions, several of those definitions coincide and the theory is rather complete. However, without compactness, the picture becomes blurry. To improve our understanding, we characterize in this work when a closed, not necessarily compact, asymptotically stable attractor on a locally compact metric space is homotopy equivalent to its domain of attraction. This enables a further structural ...