Abundance of C1-robust homoclinic tangencies
Abstract
A diffeomorphism f has a C1-robust homoclinic tangency if there is a C1-neighbourhood of f such that every diffeomorphism in g∈ has a hyperbolic set g, depending continuously on g, such that the stable and unstable manifolds of 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 C1-robust homoclinic tangencies. Using blender-horseshoes, we prove that homoclinic classes of C1-generic diffeomorphisms containing saddles with different indices and that do not admit dominated splittings (of appropriate dimensions) display C1-robust homoclinic tangencies.
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