Conley指标理论与微分包含中的吸引子-排斥子分解
动力系统
2020-09-25 v2
摘要
Conley 指标理论是描述动力系统基本结构的有力拓扑工具。该理论的一个重要特征是孤立不变集的吸引子-排斥子分解。在此分解中，不变集中的所有点属于吸引子、其相伴的对偶排斥子或连接区域。在该连接区域中，点在正向时间趋于吸引子，在反向时间趋于排斥子。该分解在某种拓扑意义下对扰动也是稳定的。Conley 理论对流和同态已发展完善，并已推广至某些更抽象的设置如半流和关系。本文旨在将吸引子-排斥子分解（包括其对扰动的稳定性）推广到连续时间集值动力系统。这类系统中最常见的是如 Filippov 系统之类的微分包含。
引用
@article{arxiv.2009.00696,
title = {Conley Index Theory and the Attractor-Repeller Decomposition for Differential Inclusions},
author = {Cameron Thieme},
journal= {arXiv preprint arXiv:2009.00696},
year = {2020}
}
备注
18 pages, 1 figure Updated Version of Article: Most importantly, several additional citations are added for works similar to this one. Additionally, a few typos are fixed ("compact" had been omitted in one key spot) and some stylistic changes (such as paragraph indentation and bibliography style) have been made. Keywords, subject classifiers, and contact information have been added