Asymptotic stability of quasi-periodic orbits

Abstract

Stability is one of the most fundamental properties of solutions to differential equations and, for example, can explain the presence of harmful vibrations. While the stability type of fixed points and periodic orbits can be assessed with standard tools, no general and reliable method allows to conclude about the stability of quasi-periodic orbits. Here, we overcome this limitation and develop a novel and universal method to rigorously assess the asymptotic stability of quasi-periodic solutions to differential equations. Furthermore, we develop an automated algorithm for such stability investigations and demonstrate its applicability on two explicit mechanical examples.