Institute of Mechanical Systems

Blow-up of Koopman eigenfunctions at basin boundaries

Abstract We show that under non-degeneracy conditions on a dynamical system, all of its smooth, non-constant Koopman eigenfunctions blow up along the boundary of the basin of attraction of a fixed point. We give a simple, geometric version of this general result for the case of a...

Existence of Spectral Submanifolds in Time Delay Systems

Abstract Spectral submanifolds (SSMs) are invariant manifolds of a dynamical system, defined by the property of being tangent to a spectral subspace of the linearized dynamics at a steady state. We show existence, along with certain desirable properties such as smoothness, attrac...