论文标题
广泛的和独特的阴影
Expansivity and unique shadowing
论文作者
论文摘要
令$ f \ colon x \ to x $成为紧凑型公制空间上的连续功能。我们表明，当地图$ f $进入时，阴影等效于向后阴影和两面阴影。使用此过程，我们继续表明，对于膨胀的过滤映射，属性阴影，双面阴影，S-Limit阴影和两侧S-Limit阴影相当。我们表明，只有当它具有独特的阴影（即，\ \ \ \ \ \ \ \ \ f $）的唯一点被遮盖时，$ f $具有阳性，并且只有在沃尔特（Walter）的证明中隐含的结果表明，阴影呈拓扑稳定。我们在双面阴影上使用上述结果，以找到对阴影和扩展性的等效表征，并将这些结果扩展到由于莫拉莱斯而引起的$ n $传播率的概念。
Let $f\colon X\to X$ be a continuous function on a compact metric space. We show that shadowing is equivalent to backwards shadowing and two-sided shadowing when the map $f$ is onto. Using this we go on to show that, for expansive surjective maps the properties shadowing, two-sided shadowing, s-limit shadowing and two-sided s-limit shadowing are equivalent. We show that $f$ is positively expansive and has shadowing if and only if it has unique shadowing (i.e.\ each pseudo-orbit is shadowed by a unique point), extending a result implicit in Walter's proof that positively expansive maps with shadowing are topologically stable. We use the aforementioned result on two-sided shadowing to find an equivalent characterisation of shadowing and expansivity and extend these results to the notion of $n$-expansivity due to Morales.
