Extending geometric singular perturbation theory to nonhyperbolic points -Fold and canard points in two dimensions

The geometric approach to singular perturbation problems is based on powerf ul methods from dynamical systems theory. These techniques have been very s uccessful in the case of normally hyperbolic critical manifolds. However, a t points where normal hyperbolicity fails, the well-developed geometric the ory does not apply. We present a method based on blow-up techniques, which leads to a rigorous geometric analysis of these problems. A detailed analys is of the extension of slow manifolds past fold points and canard points in planar systems is given. The efficient use of various charts is emphasized .