Sensitivity, local stable/unstable sets and shadowing
Dynamical Systems
2024-10-22 v3
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.
Cite
@article{arxiv.2012.08894,
title = {Sensitivity, local stable/unstable sets and shadowing},
author = {Mayara Antunes and Bernardo Carvalho and Margoth Tacuri},
journal= {arXiv preprint arXiv:2012.08894},
year = {2024}
}