论文标题
Conley索引理论和差分夹杂物的吸引子练习器分解
Conley Index Theory and the Attractor-Repeller Decomposition for Differential Inclusions
论文作者
论文摘要
康利指数理论是描述动力系统基本结构的强大拓扑工具。该理论的一个重要特征是孤立不变集的吸引者尿液分解。在这种分解中，不变集中的所有点都属于吸引子，其相关的双驱虫器或连接区域。在这个连接区域中，在向前的时间和驱虫器的后时间倾向于吸引子。在某些拓扑意义上，这种分解在扰动下也是稳定的。康利理论（Conley Theory）针对流量和同态性很好，也扩展到了一些更抽象的环境，例如半流和关系。在本文中，我们旨在将吸引子培训分解（包括其在扰动下的稳定性）扩展到连续的时间设置值的动力学系统。这些系统中最常见的是差异包含物，例如Filippov系统。
The Conley index theory is a powerful topological tool for describing the basic structure of dynamical systems. One important feature of this theory is the attractor-repeller decomposition of isolated invariant sets. In this decomposition, all points in the invariant set belong to the attractor, its associated dual repeller, or a connecting region. In this connecting region, points tend towards the attractor in forwards time and the repeller in backwards time. This decomposition is also, in a certain topological sense, stable under perturbation. Conley theory is well-developed for flows and homomorphisms, and has also been extended to some more abstract settings such as semiflows and relations. In this paper we aim to extend the attractor-repeller decomposition, including its stability under perturbation, to continuous time set-valued dynamical systems. The most common of these systems are differential inclusions such as Filippov systems.
