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Expansiveness has been used to study dynamic systems and has been developed for various forms of expansiveness. In this paper, we introduce the concept of kinematic N-expansiveness for flows on a C∞ compact connected manifold M, which is an extension of N-expansive homeomorphisms. We prove that if a vector field X on M is C1 robustly kinematic N-expansive, then it is quasi-Anosov. Furthermore, we consider the divergence-free vector fields and Hamiltonian systems with the kinematic N-expansive property; then, we study their robustness. [ABSTRACT FROM AUTHOR]

Let be a -dimensional (), compact smooth Riemannian manifold endowed with a symplectic form . In this paper, we show that, if a symplectic diffeomorphism is -robustly measure expansive, then it is Anosov and a generic measure expansive symplectic diffeomorphism is mixing Anosov. Moreover, for a Hamiltonian systems, if a Hamiltonian system is robustly measure expansive, then is Anosov. [ABSTRACT FROM AUTHOR]