Extending geometric singular perturbation theory to nonhyperbolic points -- fold and canard points in two dimensions (Q2753547)

The geometric approach to singular perturbation problems is based on methods from dynamical systems theory. These techniques are very successful in the case of normally hyperbolic critical manifolds. However, at points where normal hyperbolicity fails, the well-developed geometric theory could not be applied. The authors present a method based on blow-up techniques, that leads to a rigorous geometric analysis of these problems. A detailed analysis of fold points and canard points is given.