Generic family with robustly infinitely many sinks

We show, for every or , the existence of a Baire generic set of -families of -maps of a manifold M of dimension 2, so that for every a small the map has infinitely many sinks. When the dimension of the manifold is 3, the generic set is formed by families of diffeomorphisms. When M is the annulus, this generic set is formed by local diffeomorphisms. This is a counter example to a conjecture of Pugh and Shub.