Density of hyperbolicity and tangencies in sectional dissipative regions

In this paper we extend the notion of sectionally dissipative periodic points to arbitrarily compact invariant sets. We show that given a sectionally dissipative and attracting region for a diffeomorphisms f, there is a neighborhood of f and a dense subset of it such that any diffeomorphism g in this dense subset either exhibits a sectional dissipative homoclinic tangency or the part of the limit set of g in this attracting region is a hyperbolic compact set. The proof goes extending some results on dominated splitting obtained for compact surfaces maps.