Blenders near polynomial product maps of C-2

In this paper we show that if p is a polynomial of degree d >= 2 possessing a neutral periodic point then a product map of the form (z, w) -> (p(z), q(w)) can be approximated by polynomial skew products (z, w) -> ((p) over tilde (z, w), q(w)) possessing special dynamical objects called blenders. Moreover, these objects can be chosen to be of two types: repelling or saddle. As a consequence, such a product map belongs to the closure of the interior of two different sets: the bifurcation locus of the space of holomorphic endomorphisms of degree d of P-2 and the set of endomorphisms having an attracting set of non-empty interior Similar techniques also give the first example of an attractor with non-empty interior or of a saddle hyperbolic set which is robustly contained in the small Julia set and whose unstable manifolds are all dense in P-2. In an independent part, we use perturbations of Henon maps to obtain examples of attracting sets with repelling points and also of quasi-attractors which are not attracting sets.