abstract: joint work with Fabrizio Bianchi.
Bedford, Smillie and Ueda have introduced a notion of horn maps for polynomial diffeomorphisms of C2 with a semi parabolic fixed points, generalizing classical results from parabolic implosion in one complex variable. We prove that these horn maps satisfy a weak version of the Ahlfors island property. As a consequence, we obtain the density of repelling cycles in their Julia set, and we prove the existence of perturbations of the initial Hénon map for which the forward Julia set J+ has Hausdorff dimension arbitrarily close to 4.