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Constructing Non-Computable Julia Sets

Mark Braverman·Michael Yampolsky
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Abstract

We completely characterize the conformal radii of Siegel disks in the family $$P_θ(z)=e^{2πiθ}z+z^2,$$ corresponding to {\bf computable} parameters $θ$. As a consequence, we constructively produce quadratic polynomials with {\bf non-computable} Julia sets.

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Mark Braverman, Michael Yampolsky. 2006-04-17. Constructing Non-Computable Julia Sets. https://arxiv.org/abs/math/0604371

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