Let M be a closed n-dimensional smooth Riemannian manifold, and let X be a $C^1$-vector field of $M.$ Let $\gamma $ be a hyperbolic closed orbit of $X.$ In this paper, we show that X has the $C^1$-stably shadowing property on the chain component $C_X(\gamma )$ if and only if $C_X(\gamma )$ is the hyperbolic homoclinic class.

中文翻译：

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C1向量场具有稳定遮蔽特性的链组件

让米做一个封闭的n-维光滑黎曼流形，并且让X做一个$C^1$-向量场$M.$让$\伽马$是一个双曲闭轨道$X.$在本文中，我们表明X有$C^1$- 链组件上的稳定阴影属性$C_X(\gamma )$当且仅当$C_X(\gamma )$是双曲同宿类。