论文标题
在迭代功能系统及其拓扑稳定性上
On the Space of Iterated Function Systems and Their Topological Stability
论文作者
论文摘要
我们研究具有紧凑参数空间的迭代功能系统（IFS）。我们表明，具有相位空间的IFS $ x $的空间是自连续地图$ x $的空间的超空间。通过此结果，我们获得了Hausdorff距离是该空间的天然度量，我们用来定义拓扑稳定性。 然后，我们证明，在IFS的背景下，经典结果表明，阴影特性是拓扑稳定性的必要条件，而添加到扩展性的阴影属性是拓扑稳定性的足够条件。实际上，为了证明这些陈述，我们使用了更强类型的阴影类型，称为一致的阴影属性。 我们还举了一个例子，表明一致的阴影属性与IFS的传统属性定义确实不同。
We study iterated function systems (IFS) with compact parameter space. We show that the space of IFS with phase space $X$ is the hyperspace of the space of self continuous maps of $X$. With this result we obtain that the Hausdorff distance is a natural metric for this space which we use to define topological stability. Then we prove, in the context of IFS, the classical results showing that shadowing property is a necessary condition for topological stability and shadowing property added to expansiveness are a sufficient condition for topological stability. To prove these statements, in fact, we use a stronger type of shadowing, called concordant shadowing property. We also give an example showing that concordant shadowing property is truly different than the traditional definition of shadowing property for IFS.
