On asymptotically periodic-like motions in flows

Abstract

We study three properties associated to the recurrence of orbits in flows: asymptotic periodicity, positive asymptotic periodicity and G-asymptotic periodicity. We determine which implications between these notions hold and which do not. We also show how these notions are related to Lyapunov stability.

Keywords

• periodicity
• asymptotic periodicity
• stability.