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arXiv · 1306.2736

Quadratic polynomials, multipliers and equidistribution

Xavier Buff·Thomas Gauthier
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Abstract

Given a sequence of complex numbers ρ_n, we study the asymptotic distribution of the sets of parameters c ε C such that the quadratic maps z^2 +c has a cycle of period n and multiplier ρ_n. Assume 1/n.log|ρ_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.

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Xavier Buff, Thomas Gauthier. 2013-06-12. Quadratic polynomials, multipliers and equidistribution. https://arxiv.org/abs/1306.2736

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