Fers à cheval non uniformément hyperboliques engendrés par une bifurcation homocline et densité nulle des attracteurs

Abstract

Let f₀ be a surface diffeomorphism such that the maximal invariant set in an open set V is the union of a horseshoe and a quadratic tangency between the stable and unstable foliations of this horseshoe. We assume that the dimension of the horseshoe is larger than but close to one. We announce that, for most diffeomorphisms f close to f₀, the maximal f-invariant set in V is a non-uniformly hyperbolic horseshoe, with dynamics of the same type as met in Hénon attractors.