Distribution of Points with Proscribed Derivative in Polynomial Dynamics

Abstract : In analogy to the cquidistribntion of preimages of a proscribed point by the iterates of a polynomial map / in C towards the equilibrium measure, we show here the equidistribution of points 2 for which (fn)'(z) = a for suitable a towards the equilibrium measure. We then give a similar statement in the space of degree d polynomials for the equidistribution of parameters for which the n-derivative at a given critical value has a prescribed derivative towards the activity current of the corresponding critical point.