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Let $\{f_\mu\}_{\mu \in \mathbb{D}}$ be a family of automorphisms of$\mathbb{C}^2$ unfolding a generic homoclinic tangency associated to a fixedpoint $p$ belonging to a horseshoe. We prove that if the linearized versions ofthe Cantor sets representing the local intersections of the stable and unstablemanifolds of $p$ with the horseshoe have stable intersections, then the set ofparameters $\mu$ corresponding to automorphisms with persistent tangencies haspositive density at $\mu = 0$.

Stable intersections of Cantor sets and positive density of persistent tangencies for homoclinic bifurcations of automorphisms of $\mathbb{C}^2$