Sensitivity, local stable/unstable sets and shadowing
arXiv:2012.08894 · doi:10.1080/14689367.2023.2206545
Abstract
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.
References in corpus (6)
- On homeomorphisms with the two-sided limit shadowing property
- Hyperbolicity, transitivity and the two-sided limit shadowing property
- Beyond topological hyperbolicity: the L-shadowing property
- Positively n-expansive homeomorphisms and the L-shadowing property
- Continuum-wise hyperbolicity
- There are no stable points for continuum-wise expansive homeomorphisms