Distribution of polynomials with cycles of a given multiplier

Abstract

In 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.