Countably Expansiveness for Continuous Dynamical Systems

Manseob Lee and Jumi Oh
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Manseob Lee: Department of Mathematics, Mokwon University, Daejeon 35349, Korea
Jumi Oh: Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea

Mathematics, 2019, vol. 7, issue 12, 1-11

Abstract: 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.

Keywords: expansive; quasi-Anosov; quasi-transverality condition; Anosov (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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