Xavier Buff, Thomas Gauthier
Published 2013-06-12Version 1
Given a sequence of complex numbers {\rho}_n, we study the asymptotic distribution of the sets of parameters c {\epsilon} C such that the quadratic maps z^2 +c has a cycle of period n and multiplier {\rho}_n. Assume 1/n.log|{\rho}_n| tends to L. If L {\leq} 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.
Equidistribution speed for endomorphisms of projective spaces
New Approximations for the Area of the Mandelbrot Set
On the Laurent coefficients of the Riemann map for the complement of the Mandelbrot set
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