Preprint A355/2004
Density of hyperbolicity and homoclinic bifurcation for 3D-diffeomorphism in attracting regions.
In the present paper it is proved that given a maximal invariant attracting homoclinic class for a smooth three dimensional Kupka-Smale diffeomorphism, it follows that the homoclinic class is either hyperbolic or the diffeomorphisms is $C^1-$ approximated by another map exhibiting a homoclinic tangency or a heterodimensional cycle.