论文标题
灵敏度，本地稳定/不稳定的集合和阴影
Sensitivity, local stable/unstable sets and shadowing
论文作者
论文摘要
在本文中，我们研究了当地稳定/不稳定的敏感同构，并在紧凑的度量空间上定义了阴影特性。我们证明，本地稳定/不稳定的集合总是包含一个紧凑而完美的空间子集。作为推论，我们将结果推广到[6]和[11]中，证明在满足传递性和阴影特性的紧凑型公制空间上定义的正同态呈阳性膨胀的同态，或者只能在可计数的空间中定义。
In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space. As a corollary we generalize results in [6] and [11] proving that positively countably expansive homeomorphisms defined on compact metric spaces satisfying either transitivity and the shadowing property, or the L-shadowing property, can only be defined in countably spaces.
