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In this article we deal with singularly perturbed vector elds Z" expressed by x= F(x; y; ") if h(x; y; ") 0; G(x; y; ") if h(x; y; ") 0; "y_ = H(x; y; "); (1) where " 2 R is a small parameter, x 2 Rn; n 2; and y 2 R denote the slow and fast variables, respectively, and F, G, h and H are smooth maps. We study the eect of singular perturbations at typical singularities of Z0. Special attention will be dedicated to those points satisfying q 2 fh(x; y; 0) = 0g \ fH(x; y; 0) = 0g where F or G is tangent to fh(x; y; 0) = 0g. The persistence and the stability properties of those objects are investigated.

Singularly perturbed discontinuous vector fields