M. Krupa et P. Szmolyan, Extending geometric singular perturbation theory to nonhyperbolic points -Fold and canard points in two dimensions, SIAM J MATH, 33(2), 2001, pp. 286-314
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
.