In each manifold of dimension at least 5 we construct a vector field having a C¹ robust attractor containing a singularity and a wild hyperbolic set, in the sense of Newhouse (a hypebolic set having robut tangencies between its stable and unstable foliations). These seem to be the first examples of (C¹) robust singular attractors containing a wild hyperbolic set.

These vector fields are constructed in such a way that their dynamics reduces to the dynamics of certain endomorphisms of the punctured plane, in the same way as the dynamics of the Lorenz attractor reduces to the dynamics of an endomorphism of the punctured interval. These endomorphisms are related to the complex quadratic polynomials.

This is a joint work with R. Bamon (U. de Chile) and J. Kiwi (U. Catolica de Chile).