Equidistribution towards the bifurcation current I: multipliers and degree d polynomials

Abstract

In the moduli space \(\mathcal {P}_d\) of degree d polynomials, the set \(\text {Per}_n(w)\) of classes [f] for which f admits a cycle of exact period n and multiplier multiplier w is known to be an algebraic hypersurface. We prove that, given \(w\in {\mathbb C}\), these hypersurfaces equidistribute towards the bifurcation current as n tends to infinity.