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Countably Expansiveness for Continuous Dynamical Systems

Author

Listed:
  • Manseob Lee

    (Department of Mathematics, Mokwon University, Daejeon 35349, Korea)

  • Jumi Oh

    (Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea)

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.

Suggested Citation

  • Manseob Lee & Jumi Oh, 2019. "Countably Expansiveness for Continuous Dynamical Systems," Mathematics, MDPI, vol. 7(12), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1228-:d:297008
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