Preprint des Projektes: SFB 701: Spektrale Strukturen und Topologische Methoden in der Mathematik - Projekt B3

Numerische Analyse äquivarianter Evolutionsgleichungen

14-060 Alina Girod, Thorsten Hüls.
Nonautonomous systems with transversal homoclinic structures under discretization

We consider homoclinic orbits in continuous time nonautonomous dynamical systems. Unlike the autonomous case, stable and unstable fiber bundles that generalize stable and unstable manifolds, typically intersect transversally in isolated points. In the first part, we establish persistence and error estimates for one-step discretizations of transversal homoclinic orbits. Secondly, we extend an algorithm from England, Krauskopf, Osinga to nonautonomous systems and illustrate transversally intersecting fibers along homoclinic orbits for two examples. The first one is constructed artificially in order to study numerical errors, while the second one originates from mathematical biology.