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

Numerische Analyse äquivarianter Evolutionsgleichungen

11-011 Thorsten Hüls, Yongkui Zou.
A note on computing heteroclinic trajectories of non-autonomous maps

We propose an adequate notion of a heteroclinic trajectory in non-autonomous systems that generalizes the notion of a heteroclinic orbit of an autonomous system. A heteroclinic trajectory connects two families of semi-bounded trajectories that are bounded in backward and forward time. We apply boundary value techniques for computing one representative of each family. These approximations allow the construction of projection boundary conditions that enable the calculation of a heteroclinic trajectory with high accuracy. The resulting algorithm is applied to a non-autonomous version of Hénon's map.