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.
