The numerical detection of connecting orbits

We present a new technique for the numerical detection and localization of connecting orbits between hyperbolic invariant sets in parameter dependent dynamical systems. This method is based on set-oriented multilevel methods for the computation of invariant manifolds and it can be applied to systems of moderate dimension. The main idea of the algorithm is to detect intersections of coverings of the stable and unstable manifolds of the invariant sets on different levels of the approximation. We demonstrate the applicability of the new method by three examples.