2018/02/09 by Manseob Lee, Lee, Manseob, Jumi Oh +3
Mathematics · Physics and Astronomy · #37C05 #37C20 #37C29 #37D05 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1802.03104
openalex publication_date 2018/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In light of the rich results of expansiveness in the dynamics of diffeomorphisms, it is natural to consider another notions of expansiveness such as countably-expansive, measure expansive, N-expansive and so on. In this paper, we introduce the notion of N-expansiveness for flows on a C∞ compact connected Riemannian manifold by using the kinematic expansiveness which is extension of the N-expansive diffeomorphisms. And we prove that a vector field X on M is C1 robustly kinematic N-expansive then X satisfies quasi-Anosov. Furthermore, we consider the hyperbolicity of local dynamical systems with kinematic N-expansiveness.