Connections to fixed points and Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems - Battelli, F.; Palmer, K.J. (Український математичний журнал, 2008)
We consider a singularly perturbed system depending on two parameters with two (possibly the same) normally hyperbolic centre manifolds. We assume that the unperturbed system has an orbit connecting a hyperbolic fixed point on one centre manifold to a hyperbolic fixed point on the other. Then we prove some old and new results concerning the persistence of these connecting orbits and apply the results to find examples of systems in dimensions greater than three which possess Sil’nikov saddle-focus homoclinic orbits.