(Quadratic) polynomial skew-products are maps of the form $F (z, w) = (p(z), q(z, w))$, where $p$ and $q$ are polynomials of degree 2. These maps give the simplest non trivial examples of endomorphisms of P2(C). In this talk we investigate the natural parameter space of these maps, with emphasis on the stability-bifurcation dichotomy (that we will review in the beginning of the the seminar). In particular, we describe the geometry of the bifurcation current near infinity, and we give a partial classification of hyperbolic components. One of the tools we use is a generalisation to this setting of the one-dimensional equidistribution of some dynamically defined hypersurfaces of the parameter space towards the bifurcation current.

This is a joint work with Matthieu Astorg, Orléans.