Local Approximation of Invariant Fiber Bundles: an Algorithmic Approach

This paper contains an approach to compute Taylor approximations of invariant manifolds associated with arbitrary fixed reference solutions of nonautonomous difference equations. Our framework is sufficiently general to include, e.g., stable and unstable manifolds of periodic orbits, or classical center-stable/-unstable manifolds corresponding to equilibria. In addition, our focus is to give applicable and quantitative results. Finally, in the appendix we present a short manual to the Maple program IFB Comp to calculate Taylor approximations of invariant manifolds.