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arXiv · 1902.10444

Critical points of the multiplier map for the quadratic family

Anna Belova·Igors Gorbovickis
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Abstract

The multiplier $\lambda_n$ of a periodic orbit of period $n$ can be viewed as a (multiple-valued) algebraic function on the space of all complex quadratic polynomials $p_c(z)=z^2+c$. We provide a numerical algorithm for computing critical points of this function (i.e., points where the derivative of the multiplier with respect to the complex parameter $c$ vanishes). We use this algorithm to compute critical points of $\lambda_n$ up to period $n=10$.

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Anna Belova, Igors Gorbovickis. 2019-02-27. Critical points of the multiplier map for the quadratic family. https://arxiv.org/abs/1902.10444

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