Singular Perturbation Problems for Time-Reversible Systems

In this paper singularly perturbed reversible vector fields defined in R^2 without normal hyperbolicity conditions are discussed. The main results give conditions for the existence of infinitely many periodic orbits and heteroclinic cycles converging to singular orbits with respect to to the Hausdorff distance. Besides we classify the slow manifolds via exhibition of three normal forms on neighborhoods of non normally hyperbolic points.