We prove that every singular hyperbolic chain transitive set with a singularity does not admit the shadowing property. Using this result we show that if a star flow has the shadowing property on its chain recurrent set then it satisfies Axiom A and the no-cycle conditions; and that if a multisingular hyperbolic set has the shadowing property then it is hyperbolic.

中文翻译：

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具有奇异性的双曲奇异集的无阴影

我们证明具有奇异性的每个奇异双曲链传递集都不允许遮蔽性。利用这个结果，我们表明，如果一个恒星流在其链的递归集合上具有遮蔽特性，则它满足公理A和无循环条件；并且，如果多奇双曲集具有阴影属性，则它是双曲的。