Singularly perturbed discontinuous vector fields

Resumo

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.