Blenders near polynomial product maps of C².

In this paper we show that if p is a polynomial which bifurcates then the product map (z,w)↦(p(z),q(w)) can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets can be chosen to be of two types: repelling or saddle. As a consequence, such product map belongs to the closure of the interior of two different sets: the bifurcation locus of Hd(P²) and the set of endomorphisms having an attracting set of non-empty interior. In an independent part, we use perturbations of Hénon maps to obtain examples of attracting sets with repelling points and also of quasi-attractors which are not attracting sets. [ABSTRACT FROM AUTHOR]