ABUNDANCE OF C1-ROBUST HOMOCLINIC TANGENCIES

A diffeomorphism f has a C-1-robust homoclinic tangency if there is a C-1-neighborhood U of f such that every diffeomorphism in g is an element of U has a hyperbolic set Lambda(g), depending continuously on g, such that the stable and unstable le manifolds of Lambda(g), have some non-transverse intersection. For every manifold of dimension greater than or equal to three we exhibit a local mechanism (blender-horseshoes) generating diffeomorphisms with C-1-robust homoclinic tangencies. Using blender-horseshoes, we prove that homoclinic classes of C-1-generic diffeomorphisms containing saddles with different indices and that do not admit dominated splittings (of appropriate dimensions) display C-1-robust homoclinic tangencies.