%0 Journal Article
%T Countably Expansiveness for Continuous Dynamical Systems
%J Mathematics | An Open Access Journal from MDPI
%D 2019
%R https://doi.org/10.3390/math7121228
%X Expansiveness is very closely related to the stability theory of the dynamical systems. It is natural to consider various types of expansiveness such as countably-expansive, measure expansive, N-expansive, and so on. In this article, we introduce the new concept of countably expansiveness for continuous dynamical systems on a compact connected smooth manifold M by using the dense set D of M, which is different from the weak expansive flows. We establish some examples having the countably expansive property, and we prove that if a vector field X of M is C 1 stably countably expansive then it is quasi-Anosov. View Full-Tex
%U https://www.mdpi.com/2227-7390/7/12/1228