Preprint A432/2006
Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets

Enrique R. Pujals

**Keywords: **

Given a topologically hyperbolic attracting set of a smooth three dimensional Kupka-Smale diffeomorphism, it is proved under some hypothesis over the dissipation rate, that the set is either hyperbolic or the
diffeomorphisms is $C^1-$ approximated by another one exhibiting either a
heterodimensional cycle or a homoclinic tangency.