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A parameter c 0 ∈ C in the family of quadratic polynomials f c (z) = z 2 + c is a critical point of a period n multiplier, if the map f c0 has a periodic orbit of period n, whose multiplier, viewed as a locally analytic function of c, has a vanishing derivative at c = c 0 . We prove that all critical points of period n multipliers equidistribute on the boundary of the Mandelbrot set, as n → ∞.

We give a topological model of the critical locus for complex Hénon maps that are perturbations of the quadratic polynomial with disconnected Julia set.

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