Distribution of polynomials with cycles of a given multiplier

International audienceIn the space of degree d polynomials, the hypersurfaces defined by the existence of a cycle of period n, and multiplier e(i theta) are known to be contained in the bifurcation locus. We prove that these hypersurfaces equidistribute the bifurcation current. This is a new result, even for the space of quadratic polynomials