The dynamics of slow manifolds

Invited lecture at Konferensi Nasional Matematika XIII, Semarang, 24-27 juli, 2006; to be publ. in J. Indones. Math. Soc. (2007) After reviewing a number of results from geometric singular perturbation theory, we discuss several approaches to obtain periodic solutions in a slow manifold. Regarding nonhyperbolic transitions we consider relaxation oscillations and canard-like solutions. The results are illustrated by prey-predator systems