Finite dimensional approximations of dynamical systems generated by delay equations

Abstract

In this thesis, we study three different approximation methods. First, we study the pseudospectral approximation method, where we approximate eigenvalues of delay equations. Moreover, we look at the parametrisation method, which we can use to approximate invariant manifolds of both finite and infinite dimensional dynamical systems. Lastly, we study Trotter-Kato approximation methods, where we approximate flows and orbits of delay equations.