AI 中文总结
研究随机动力系统的拓扑稳定性，通过随机连续扩张性和跟踪性概念扩展经典结果，证明相关系统随机拓扑稳定，还建立性质共轭下拓扑不变性并分析拓扑传递性与周期跟踪性的关系。
AI 中文摘要
本文研究随机动力系统的拓扑稳定性。主要目标是通过运用随机连续扩张性和跟踪性的概念，将Walters的经典结果扩展到随机情形。证明了任何随机 \(cw -\) 扩张且满足随机跟踪性的随机动力系统是随机拓扑稳定的。此外，在随机情形下建立了这些性质在共轭下的拓扑不变性，并分析了拓扑传递性与周期跟踪性之间的关系。
英文摘要
This paper investigates the topological stability of random dynamical systems . Our main goal is to extend the classical result of Walters \cite{Walters77} to the random setting by employing the notions of random continuum-wise expansivity and shadowing property. We prove that any random dynamical system that is random $cw$-expansive and satisfies the random shadowing property is randomly topologically stable. Furthermore, in the random setting we establish the topological invariance of these properties under conjugacy and analyze the relationship between topological transitivity and the periodic shadowing property.
