We show that every pointwise persistent homeomorphism with the shadowing property is persistent. The proof relies on a new tracing property, the persistent shadowing property , which has its own interest. We shown for instance that expansive homeomorphisms with this property are s-topologically stable in the sense of Kawaguchi (Discrete Contin Dyn Syst 39(5):2743–2761, 2019). We also present orbital versions of our results.

中文翻译：

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逐点持久性和阴影

我们证明了每个具有阴影属性的逐点持久同胚都是持久的。证明依赖于一个新的跟踪属性，持久阴影属性，它有自己的兴趣。例如，我们证明了具有这种性质的膨胀同胚在 Kawaguchi 的意义上是 s 拓扑稳定的（Discrete Contin Dyn Syst 39(5):2743–2761, 2019）。我们还展示了我们结果的轨道版本。