Quadratic polynomials, multipliers and equidistribution
Abstract
Given a sequence of complex numbers n, we study the asymptotic distribution of the sets of parameters c ε C such that the quadratic maps z2 +c has a cycle of period n and multiplier n. Assume 1/n.log|n| tends to L. If L ≤ log 2, they equidistribute on the boundary of the Mandelbrot set. If L > log 2 they equidistribute on the equipotential of the Mandelbrot set of level 2L - 2 log 2.
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