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Countably Expansiveness for Continuous Dynamical Systems

by Manseob Lee 1 and Jumi Oh 2,*
Department of Mathematics, Mokwon University, Daejeon 35349, Korea
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1228;
Received: 29 October 2019 / Revised: 8 December 2019 / Accepted: 9 December 2019 / Published: 12 December 2019
(This article belongs to the Section Mathematics and Computer Science)
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-Text
Keywords: expansive; quasi-Anosov; quasi-transverality condition; Anosov expansive; quasi-Anosov; quasi-transverality condition; Anosov
MDPI and ACS Style

Lee, M.; Oh, J. Countably Expansiveness for Continuous Dynamical Systems. Mathematics 2019, 7, 1228.

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