Newhouse phenomenon for automorphisms of low degree in [formula omitted

Abstract

We show that there exists a polynomial automorphism f of C3 of degree 2 such that for every automorphism g sufficiently close to f, g admits a tangency between the stable and unstable laminations of some hyperbolic set. As a consequence, for each d≥2, there exists an open set of polynomial automorphisms of degree at most d in which the automorphisms having infinitely many sinks are dense. To prove these results, we give a complex analogous to the notion of blender introduced by Bonatti and Díaz.