This will be an introductory lecture to recently developed methods of geometric singular perturbation theory. The basic notion of a slow manifold and attendant stable and unstable manifolds will be discussed. The Fenichel Normal Form is a coordinate system tailored to the behavior near the slow manifold and its encapsulation of the local geometry will be explained. Examples and challenges will be presented as well as an explanation given as to how shooting arguments are now viewed through the tracking of invariant manifolds.
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