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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.
T. Gauthier, G. Vigny. Distribution of Points with Proscribed Derivative in Polynomial Dynamics. Rivista di Matematica della Universita di Parma, 2017, 8 (2), pp.247--270. ⟨hal-03700892⟩