Hopf bifurcations and homoclinic tangencies

In this paper we prove that a diffeomorphism with a homoclinic orbit associated to a generic Hopf bifurcation point can be perturbed to obtain a homoclinic tangency. Let [F-t] be a generic one-parameter family of diffeomorphisms that unfolds a Hopf bifurcation point which has associated a transverse homoclinic point. For this kind of family we prove also that F-t can be perturbed to obtain a homoclinic tangency for that t such that the rotation number of F-t restricted to the invariant circle, produced by the Hopf bifurcation, is irrational.