Preprint 15/97 in the DFG-Schwerpunktprogramm "Ergodentheorie, Analysis und effiziente Simulation dynamischer Systeme":

W.-J. Beyn, M. Stiefenhofer: A direct approach to homoclinic orbits in the fast dynamics of singularly perturbed systems

Homoclinic orbits in the fast dynamics of singular perturbation problems are usually analyzed by a combination of Fenichel's invariant manifold theory with general transversality arguments (the Exchange Lemma). In this paper an alternative direct approach is developed which uses a two-time scaling and a contraction argument in exponentially weighted spaces. Homoclinic orbits with one fast transition are treated and it is shown how epsilon-expansions can be extracted rigorously from this approach. The result is applied to a singularly perturbed Bogdanov point in the FitzHugh-Nagumo system.

preprint_15_97.ps.gz (294KB, includes 3 illustrations)  preprint_15_97.ps (6MB (!), includes 3 illustrations)

Other preprints in the DFG-Project Connecting Orbits.

DFG-Project Connecting Orbits (Bielefeld)

DFG-Schwerpunktprogramm Dynamik (Berlin)

Department of Mathematics | University of Bielefeld