On inclination-flip homoclinic orbit associated to a saddle-node singularity

In this article, we study vector fields bifurcating through a saddlenode equilibrium with an unstable homiclinic orbit. Bifurcating diagrams for two-parameter perturbations of these vector fields are exhibited. It is proved that Smale's horseshoe dynamics, surrounding the bifurcating homoclinic orbit, exists for a large set of such perturbations.Partially supported by CNPq-Brazil and CONICIT-Venezuela.