First homoclinic tangencies in the boundary of Anosov diffeomorphisms (Q1576803)

Let \(f:M\to M\) be an Anosov diffeomorphism on a compact connected Riemannian manifold \(M\) of dimension two. The main goal of this note is the analysis of the generic ways \(f\) has to lose hyperbolicity and the construction of a path, from \(f\) to the boundary of its stability component, that ends with a diffeomorphism exhibiting a cubic homoclinic tangency.