亏格p曲面上二维系统的不稳定解及纽结吸引子的拓扑
Inversely Unstable Solutions of Two-Dimensional Systems on Genus-p Surfaces and the Topology of Knotted Attractors
摘要：
在本文中，我们将表明，一个周期性的非线性，时变耗散系统，是定义在亏格-p表面包含一个或多个不变集作为吸引子。此外，我们将推广[Martins，2004]中的一个结果，并给出条件下，这些不变集是不是同胚的一个圆圈，这意味着存在的混沌行为。这是通过研究每个不变集内的逆不稳定解的出现来实现的。
英文摘要：
In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins, 2004] and give conditions under which these invariant sets are not homeomorphic to a circle individually, which implies the existence of chaotic behaviour. This is achieved by studying the appearance of inversely unstable solutions within each invariant set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
