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arXiv · 1903.00062

Equidistribution of critical points of the multipliers in the quadratic family

Tanya Firsova·Igors Gorbovickis
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Abstract

A parameter $c_0\in\mathbb C$ in the family of quadratic polynomials $f_c(z)=z^2+c$ is a critical point of a period $n$ multiplier, if the map $f_{c_0}$ 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 $n\to\infty$.

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Tanya Firsova, Igors Gorbovickis. 2019-02-28. Equidistribution of critical points of the multipliers in the quadratic family. https://arxiv.org/abs/1903.00062

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