Kinematic N-expansive continuous dynamical systems

Abstract

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.