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 [Formula: see text]-expansiveness for flows on a [Formula: see text] compact connected manifold [Formula: see text], which is an extension of [Formula: see text]-expansive homeomorphisms. We prove that if a vector field [Formula: see text] on [Formula: see text] is [Formula: see text] robustly kinematic [Formula: see text]-expansive, then it is quasi-Anosov. Furthermore, we consider the divergence-free vector fields and Hamiltonian systems with the kinematic [Formula: see text]-expansive property; then, we study their robustness.